integration class q

[grim rampart]

how do you integrate

[buoyant pine]

im not sure, my teacher showd us this but we have never done it

im a first year a level studet so i am finding it hard to keep up wtih second year classes,i just need a good enough person to teach me how to do it.

[grim rampart]

ok so integration

do you know how differentiation works

[buoyant pine]

yea

[grim rampart]

ok so how would you differentiate a*x^n

[fossil pier]

I'm gonna listen to this as well

[grim rampart]

nice

[buoyant pine]

what does that mean

the hsh

hash

[grim rampart]

what

[fossil pier]

Times

I think he meant the asterisk

[gentle lava]

a times x to the nth power

[grim rampart]

^

[buoyant pine]

im not sure how to do this all i know is like

u add one to the power

and remove one from the digit

and it follows from dy/dx

[gentle lava]

add one and divide by the new power

[fossil pier]

an*x^n-1

[gentle lava]

opposite to differentiation

[grim rampart]

ok so differentiating

[gentle lava]

anyways I'll shut up and go away

[grim rampart]

is times by the power, reduce the power by 1

so eg differentiating a times x^n

times by the power so an x^n

reduce the power by 1 so an x^(n-1)

cool?

[buoyant pine]

yea

oh that makes sense

[grim rampart]

integration works the same but backwards

integration is add 1 to the power, and divide by the new power

so integrating a x^n

would be what kenzo

[fossil pier]

Cool stuff

[buoyant pine]

it would be x*n^2/2

?

[grim rampart]

nop

[fossil pier]

(ax^n+1)÷(n+1)?

[grim rampart]

which bit is the power

im asking kenzo

[buoyant pine]

isnt it n?

[grim rampart]

yep

[buoyant pine]

then 2 n's make

[grim rampart]

so if you added one to it

[fossil pier]

I'm Kenzo 2

[buoyant pine]

n squared

or

n plus 1

?

[grim rampart]

n+1 yep

[buoyant pine]

so

[grim rampart]

so a x^(n+1)

then

[buoyant pine]

will it be x^(n+1) then divide it by

n+1

[grim rampart]

yep

[buoyant pine]

aye!

[grim rampart]

a x^(n+1) / (n+1)

ok so

[buoyant pine]

who is a?

where is a?

coming from

[grim rampart]

a is a multiple of it

im gonna do an example with you

[buoyant pine]

multiple of what?

[grim rampart]

x^n

[buoyant pine]

can we try that one?

[grim rampart]

so for example

[fossil pier]

The number before x like 2x²

[grim rampart]

can you differentiate x^3, and 5x^4

[buoyant pine]

so this isnt integrate

hrm

[grim rampart]

its the other one

[buoyant pine]

so x^3 x ^3 so x^5

[grim rampart]

what

[buoyant pine]

wait

[grim rampart]

what was the process for differentiating

2 steps

[buoyant pine]

erm like

times by power

and then

[grim rampart]

.

[buoyant pine]

remove by 1

[grim rampart]

yep

so for x^3

do the first step

what happens

[buoyant pine]

so do i just multiply it again so x^6?

[grim rampart]

multiply by the power means

times the thing by what the power is

so its 3 * x^3

[buoyant pine]

so x^9

[grim rampart]

no

[buoyant pine]

3x

[grim rampart]

no

its just 3x^3

[buoyant pine]

^9

why doesnt the power move

[grim rampart]

because its a power not being multiplied

if i times 2^2 by 3 it doesnt become 6^6

its 3 times 2^2

[buoyant pine]

then reduce power by one so

3x^2

[grim rampart]

ep

yep

ok how about 5 x^4

[buoyant pine]

alright so

[grim rampart]

again whats the steps

[buoyant pine]

multiply by power and reduce power by 1

s

5x4 = 20 so 20x^3 (reduce by 1)]

[grim rampart]

perfect

last q as a tester

differentiate 6 x^70

[fossil pier]

Testing bro's mental maths

[buoyant pine]

so 420^69 ?

[grim rampart]

haha nice

[gentle lava]

😭

[grim rampart]

you missed the x but

420 x^69

[buoyant pine]

sorry

[grim rampart]

blaze it

[fossil pier]

Ffs

[grim rampart]

anyway ok so thats differentiating

[fossil pier]

I got the answer but didn't see the joke

[grim rampart]

now lets do integrating

for me integrate 6x^2 and 8x and 10x^3

[buoyant pine]

what are the steps again

[grim rampart]

so its differentiating but backwarsd

its add one to the power, then divide by the new power

do you see how if you do this backwards, and do the opposite of each instruction

its differentinatin

[buoyant pine]

ok so 6x^3/x^3 ?

or

divide by 3

[gentle lava]

divide by 3

[grim rampart]

by what the power is

so 3

[buoyant pine]

6x^3 divide by 3

yeaaa

[grim rampart]

simplify

[fossil pier]

2x³

He's cooking

[buoyant pine]

so

3 and 2

[grim rampart]

for spectators we have quite the rowdy chat

[buoyant pine]

2x^2?

3

[grim rampart]

yep

[buoyant pine]

2x^2

[grim rampart]

how about 8x

[buoyant pine]

3

erm

wait

[grim rampart]

2x^3 was right

[buoyant pine]

so 8x^2/2

[gentle lava]

(constant of integration??)

[grim rampart]

im ignoring it for now

[grim rampart]

again

[gentle lava]

o okay

[grim rampart]

simplify

[buoyant pine]

4x^2

[grim rampart]

nice

and then 10x^3

[fossil pier]

Dm me what that is

[buoyant pine]

10x^4/4

[grim rampart]

im gonna say it again

[buoyant pine]

hrm?

[grim rampart]

SIMPLIFY

[gentle lava]

• c

[buoyant pine]

5x^4/2

?

idk

[grim rampart]

nice perfect

[buoyant pine]

that ones hader

[grim rampart]

ok so

[fossil pier]

Oh is it because we don't know what the integer is?

[gentle lava]

want a pretty picture of where it comes from

[gentle lava]

I mean yes that's true

[grim rampart]

theres letters but dont let them scare you

the middle thing is saying

[buoyant pine]

is it okay if u guys go into personal message because im struggling with maths here

[gentle lava]

my apologies

[grim rampart]

'integrate ax^2 - 7a^2 x - 7a^3 / 3'

[fossil pier]

Sure

[buoyant pine]

yea

[grim rampart]

so

we can do this term by term

so ax^2

integrate

[buoyant pine]

ax^3/3

[grim rampart]

nice

next one

-7a^2 x

[buoyant pine]

-7a^3x/3x

[grim rampart]

nop

[buoyant pine]

cry

[grim rampart]

so x is the variable youre integrating

[fossil pier]

Is it only the X that is affected or coefficient of a as well?

[grim rampart]

a is just an extra thing

[grim rampart]

affected by what

[buoyant pine]

so 3x^2/2

[grim rampart]

youve lost the rest of the variables

[fossil pier]

Like I know that the power of X is increased

But is power of a also increased?

[grim rampart]

integrating -7a^2 x

[grim rampart]

no

integrating -7a^2 x

[fossil pier]

Cool

[grim rampart]

you do the rules for x

ignore everything else for now

[buoyant pine]

wait

-7xa^3/3

[grim rampart]

you did the rules for a

not x

[buoyant pine]

what do i do

i dont get it

[grim rampart]

whats the power of x

[buoyant pine]

2

3

[grim rampart]

no

[buoyant pine]

wait

[grim rampart]

integrating -7a^2 x

[buoyant pine]

1

cuz

[grim rampart]

yea

so

do the rules

after step 1 what happens

[buoyant pine]

-7xa^3x^2/(3x2)

=6

[grim rampart]

not over 3x2

you divide by the power of x

again you ignore a

[buoyant pine]

so 1

[grim rampart]

so 2

[buoyant pine]

wait xuz

cuz

x power is 1

[grim rampart]

-7a^2 x

[buoyant pine]

add 1 to it

[grim rampart]

add one to the power

[buoyant pine]

is 2

[grim rampart]

-7a^2 x^2

divide by the new power

-7a^2 x^2 / 2

[buoyant pine]

so -7xa^2x^2/2

[grim rampart]

use * for times

cuz x is a varaible

but yes

[buoyant pine]

okok i get it

dang this is tricky

[grim rampart]

ok and then

im gonna do a different example first

how would you integrate just the number 1

[buoyant pine]

1^2/2

[grim rampart]

nop

[buoyant pine]

cuz 1^1 is 1

no?

[grim rampart]

yeah but its not the power of 1 that matters

its the power of x

so im gonna say

[fossil pier]

Maths is fun

[grim rampart]

do you know what x^0 is

[buoyant pine]

not sure

[grim rampart]

so anything to the power of 0

is 1

[buoyant pine]

always?

even negative

[grim rampart]

always

yea

so we can rewrite 1 as

1 * x^0

right

[buoyant pine]

I SEE

so

1^1/1 = 1

[grim rampart]

wheres x gone

[buoyant pine]

maybe i dont see

[grim rampart]

what have you done with the power of x

[buoyant pine]

isnt it jus integrating 1

[grim rampart]

1 x^0

im saying 1 = 1 * x^0

[buoyant pine]

1x^1/1

[grim rampart]

because x^0 = 1

yep

[buoyant pine]

ohhh ok i get it

[grim rampart]

simplified is just x

[buoyant pine]

damn this stuff is harddd how will i learn all this in a year :/

[grim rampart]

ok try integrate 4

[fossil pier]

Are you sitting Alevel maths paper at the end of year 12?

[buoyant pine]

4x^1/1

[buoyant pine]

yeah

[fossil pier]

Damn

[grim rampart]

simplify

[fossil pier]

How come you don't get the full 2 years?

[buoyant pine]

4x.

[grim rampart]

ok integrate 100

[buoyant pine]

becayse its

100x^1/1 = 100x

[grim rampart]

ok so let say i have a mysterious constant called c

(c is NOT x)

integrate c (use same method you just used)

[buoyant pine]

who is c

[grim rampart]

.

[buoyant pine]

what u mean constant

[grim rampart]

a number that you dont know

but its fixed

ie it cant change

[buoyant pine]

how will i work it out if i dnt know

oh

0?

[grim rampart]

no

do the exact same method you did for 1, 4 and 100

for c

integrating

[buoyant pine]

100x^1/1 = 100x +c

c = unknown

so

[grim rampart]

where the fuck has 100 come from

and +c

[buoyant pine]

i have no idea

[grim rampart]

integrate 4 for me

[buoyant pine]

4x^1/1

[grim rampart]

simplify

[buoyant pine]

4x

[grim rampart]

integrate 9

[buoyant pine]

9x

[grim rampart]

do the exact same method

integrate c

where c is a constant

[buoyant pine]

c multiplinksd by x

[grim rampart]

yep

[buoyant pine]

cx

[grim rampart]

cx

so a rule is

constants integrate to

x times the constant

ok

does that make sense

[buoyant pine]

yeah

[grim rampart]

ok so knowing that

integrate:

do not overcomplicate this

[buoyant pine]

• 7a^4/4

[grim rampart]

nope

remember its not a we are integrating

its 'x'

yeah

[buoyant pine]

so

7^1*a^3/1

[grim rampart]

this is a consatnt right

a is a consatnt

[buoyant pine]

so

[buoyant pine]

i dont really understand that statement

c integrates

to x tmes the constant

so x is 1

so x c c

[grim rampart]

no

[buoyant pine]

x x c

[fossil pier]

Basically whenever you see a term or any letter or number without X in it

[grim rampart]

theyre not being equated

[fossil pier]

Times it by x

[grim rampart]

you are integrating to it

[buoyant pine]

can u gimme an example like this w diff numbers

cuz if x = 1

[grim rampart]

integrate 9

[buoyant pine]

9x

[grim rampart]

integrate 100

[buoyant pine]

100x

[grim rampart]

integrate c

[buoyant pine]

cx

[grim rampart]

integrate -7a^3 / 3

[fossil pier]

-∞d⁴ integrated is -∞d⁴x

[grim rampart]

do the exact same thing

you did with the other 3

to this

[buoyant pine]

-7^1a^3x1 / 3x1

[grim rampart]

its (-7a^3 / 3) x

[buoyant pine]

gimme a diff example

ill do it

[grim rampart]

integrate b

[buoyant pine]

bx

[grim rampart]

integrate a

[buoyant pine]

no like w the minuses

[grim rampart]

integrate -a

[buoyant pine]

the big numbers scare me its hard to work around

-ax

[grim rampart]

integrate -7a

[buoyant pine]

-7ax

[grim rampart]

integrate -7a^3

you are thinking too much

[buoyant pine]

-7a^4/4 + c

x c?

[grim rampart]

nope

what did you do for literally every other integral you did in the past minute

do that again

you should be able to do this with no thinking

[buoyant pine]

-7a^31/31

[grim rampart]

nope

integrate a

[buoyant pine]

i jus came from gcse its hard

wait

-21^4/4

[grim rampart]

the fact you are thinking means youre doing too much

no

integrate a

[buoyant pine]

ax

[grim rampart]

how did you do that

what did you do

to get that

[buoyant pine]

a times x

[grim rampart]

nice

integrate -a

[buoyant pine]

-ax

[grim rampart]

nice how did you do that

[buoyant pine]

-a timesx

[grim rampart]

ok integrate -7a

[buoyant pine]

-7^1*a/1

[grim rampart]

nope

[buoyant pine]

wait so

-7 = x

[grim rampart]

nope

x is a variable you cant control

-7a integrates to -7ax

[buoyant pine]

-7a times by x

[grim rampart]

yes

whats been the pattern for all of these

[buoyant pine]

we timesing by x

[grim rampart]

ok so

without thinking at all

integrate -7a^3

[buoyant pine]

-7a^3x

[grim rampart]

perfect

you do the funny business about

adding 1 to the power and dividing by the new powe

when x is already in the equation

x is not in -7a^3

so its just -7a^3 x

[buoyant pine]

so are x and c different

[grim rampart]

x is a variable

c is a constant

[buoyant pine]

i see

[grim rampart]

x can be anything and vary, c can be anything but is fixed to what it is

ok lastly

integrate -7a^3 /3

[buoyant pine]

-7a^3/3x

[grim rampart]

awesome

note that x isnt in the denominator

[buoyant pine]

is that it

[fossil pier]

I came

[buoyant pine]

ye'

[grim rampart]

yeah thats it

[buoyant pine]

its outside

because its not in the dividing thing

its just the variabler

[grim rampart]

see what i mean about you thinking too much

[buoyant pine]

sorry..

[grim rampart]

it looks gross

[fossil pier]

Examples because I got bored

[grim rampart]

but its 0 thinking

its nw

can you like fuck off

i dont care

[covert moat]

mister monster is literally the goat man

[grim rampart]

thanks

[fossil pier]

I'm just showing him calm down buddy

[grim rampart]

anyway so

bro you got your dick and balls out in this chat while im trying to help

ok so integrating the whole thing

you just mash them together with adding / subtracting

ok

[buoyant pine]

ill try but mashing together is that like expandintion

[fossil pier]

Dick and balls reveal!?

[grim rampart]

ill show you an easier example first

so eg

can you quickly integrate x^2 and 9 for me

seperately

[buoyant pine]

x^2 x and 9x

[grim rampart]

ah i see ive over simplified

so 9x is right

you need to do the

[buoyant pine]

oh wait

[grim rampart]

add 1 to the power, divide by the new power

for x^2

[buoyant pine]

x^3/3 x

[grim rampart]

x^3 / 3 is right

no x on the end when doing the other thing

[buoyant pine]

wait wdym

when doiung the

[grim rampart]

when doing the add 1 to the power, divide by the new power

dont put x on the end

[buoyant pine]

add divide thing u dont add the x?

ohk i didnty know sorry

so

x^3/3 and 9x

[grim rampart]

when its just a constant like 9 or a or -7a^3 /3

you just stick x on the end

yep

now again

dont overcomplicate

what do you think integrating x^2 + 9 will be

think simple

[buoyant pine]

hrrrrr wouldnt it just be x^3/ 3?

• 9

[grim rampart]

• 9x

[buoyant pine]

and the 9x is. thwe x

[grim rampart]

its x^3 / 3 + 9x

[buoyant pine]

yeah thats what i was thinking

[grim rampart]

its just them integrated seperately

added together

[buoyant pine]

i see

so for example like

[grim rampart]

easy peasy right

[buoyant pine]

x^9 +42 is like

x^10/10 +42x

[grim rampart]

perfect

how about x^2 + 2x

integrating that

[buoyant pine]

but theres already an x

[grim rampart]

yep

so dont just stick x on the end

[buoyant pine]

x^3/3 + 2x

its already

x'd

[grim rampart]

remember the steps when you have x

its increase the power by 1

divide by the new power

yeah

[buoyant pine]

i have to do it for 2x as well?

[grim rampart]

yeah

[buoyant pine]

oh

[grim rampart]

if its not a constant, do the steps always

[buoyant pine]

so it only is just *(x) when its a single integer like whole but when theres an X its like a seperate integeration whenever he is coming

with the number

[grim rampart]

its *x when there isnt already x there

so eg 3, c, -7a, pi

[buoyant pine]

okkk

[grim rampart]

none of them have x

so its just *x

[buoyant pine]

ahhh. thats why it become cx

okok

[grim rampart]

yea

now 2x

already has x

so its not just times x

its the other one

[buoyant pine]

2x^2

[grim rampart]

perfect

so integrate x^2 + 2x

[buoyant pine]

x^3/3 + 2x^2/2 ya?

[grim rampart]

simplify please

x^3 / 3 is good

2x^2 / 2 can be simplified

[buoyant pine]

is it just

x^2

[grim rampart]

yep

ok so

[buoyant pine]

i suck at simplifing

take me ages

[grim rampart]

be careful

and feel free to tell me the steps

integrate this

remember only do the rules and stuff to x not to anything else

[buoyant pine]

becaude he have x already ax^3/3

[grim rampart]

perfect

[buoyant pine]

-7a^2*x^1/1 because him already having x

[grim rampart]

so yes we already have x

[buoyant pine]

last guy he just having 7a^3/3 x

[grim rampart]

youve done the power wrong tho

last one is good

[buoyant pine]

because he no habing x

hrm

let me see

-7a^2x^2/2

[grim rampart]

perfect

so all together?

[buoyant pine]

okk lets go!

its am

ax^3/3 - -7a^2x^2/2 - 7a^3/3 x

[grim rampart]

perfect

[buoyant pine]

with the minis signs

[grim rampart]

ive written like this because i find it easier to read

[buoyant pine]

yaa

[grim rampart]

ok cool

integration part done

reposting question

so this bit

[buoyant pine]

who is him ?

[grim rampart]

if you ignore the a^2 and a

[buoyant pine]

f

[grim rampart]

means 'integrate the thing you just integrated'

look up 1 line

[buoyant pine]

ys

so erm

[grim rampart]

now the a^2 and a

are whats called

limits of integration

[buoyant pine]

so maximum and minimums?

[grim rampart]

we will do an example first beacuse its easier with example

not max and min as such

[buoyant pine]

okok

[grim rampart]

i will show

this

is fancy talk for

'integrate x^2'

the d'x' tells you

'do the integrating to the letter x'

(not any other letter)

and the big S thing means integrate

ok?

[buoyant pine]

cry

[grim rampart]

so we can say

right

[buoyant pine]

yaaa

[grim rampart]

its just writing down what weve just done

in the fancy symbols

ok

[buoyant pine]

because we only integrating x not dx because we not know him and we no no f

jus the x

[grim rampart]

ignore the question for now

[buoyant pine]

ok

ohk

so this one doesnt affect it

the symbols is it

[buoyant pine]

f means integrate

dx is the integrate the letter x

[buoyant pine]

so i try this one

[grim rampart]

solve that

yep

[buoyant pine]

10x^5/5

[grim rampart]

simplify

always simplify

[buoyant pine]

2x^5

[grim rampart]

nice

awesome

now im gonna add in the limits

so eg itll look like

see how ive got the

3 and 1 now

[buoyant pine]

yaa

[grim rampart]

so this says

after doing the integrating as normal

plug in the 3 and the 1 seperately for x

and do first - second

ill show

[buoyant pine]

who am i plug into

[grim rampart]

so after the =

ive just written what you got the integral as

[buoyant pine]

i get it

[grim rampart]

and then under

ive replaced x with 3 and 1

and done a subtraction

ok

[buoyant pine]

so x him is go now we put inside the number subtitute

den is a top limit - bottom limit

[grim rampart]

exactly

here is full working

[buoyant pine]

i see, that makes sense

[grim rampart]

solve this

or rather evaluate this

[buoyant pine]

= 3x^3/3 - x^3

so

[grim rampart]

then what

after x^3

[buoyant pine]

(3(4)^3)-(3(2)^3) = 192 - 24 = 168

[grim rampart]

nope so

you integrated to just x^3

not 3x^3

[buoyant pine]

((4)^3) - ((2)^3) =

64 - 8

• 56

[grim rampart]

nice

last example

evaluate this

[buoyant pine]

x^4/4

so

((4)^4/4) - ((1)^4/4) = 3

[grim rampart]

doesnt = 3

but what you wrote in brackets is correct

[buoyant pine]

4 minus

[grim rampart]

nope

[buoyant pine]

it comes as 4-1 for me

[grim rampart]

youre typing it in wrong then

[buoyant pine]

oh i wrote

to the power of 4/4

[grim rampart]

yeah thats not right

[buoyant pine]

i meant to put in my calculator

over 4

[grim rampart]

yeah i know

anyway

i think you have grasped the idea

[buoyant pine]

lets try the real q?

or is there something else i need

[grim rampart]

now im gonna remind you

that the q uses letters

but DONT change your method

works exactly the same

youve already done the integrating

[buoyant pine]

now what

jus

input

into

the bounds

limits

[grim rampart]

yep

[buoyant pine]

ax^3/3 - -7a^2x^2/2 - 7a^3/3 x (edited)

so do i do it for all / each of them them redo it for the minimum one too

[grim rampart]

yeah

so ive done it over 2 lines

because its so long

but its one big subtraction

[buoyant pine]

ive only got to line 2 so far

1

[grim rampart]

ok

[buoyant pine]

now is it expandig

[grim rampart]

yep

[buoyant pine]

cuz i got to line 2

how u did

[grim rampart]

i really hope you know your index laws

[buoyant pine]

erm

i know 2

[grim rampart]

which 2

[buoyant pine]

the a^(m) x a^(n) = a(m+n)

[grim rampart]

yep

[buoyant pine]

and the

[grim rampart]

is the other one the dividing one

[buoyant pine]

addition one

nah idk the others

[grim rampart]

whats the addition one

[buoyant pine]

same base can be added or sum

[grim rampart]

ok so theres another useful one

that im just gonna tell you

(a^m)^n = a^(m times n)

im ngl this question looks aids

[buoyant pine]

who is that]

for letter a?

yeah foil isnt working here

[buoyant pine]

i got like some crazg number like 5400x^8/24

yh i got this

but

when i added the together

i got like

5400

lol

[grim rampart]

you cant add them with different powers

that is how it is simplified

[buoyant pine]

then what is onwaards from here

[grim rampart]

well mostly simplified

first of all the last 3 terms are all

a^4 stuff

so you can combine them into

this

and then the question states that

this is = 0

[buoyant pine]

so like the final answer is 0???

[grim rampart]

nope

means you have this equation

so you just solve that

[buoyant pine]

what is it solved down to?

i dont understand this from here onwards

[grim rampart]

i think you should

[buoyant pine]

can u add colours pls cuz it helps alot

[grim rampart]

revise and work on the rest of the spec

this question is too hard for you based on your current understanding

theres not really any point in finishing the question from here

[buoyant pine]

i will reviseit but

[grim rampart]

you should do practice problems and stuff to get better

[buoyant pine]

can u help me just complete that last aprt

like to find out a

i ended up getting -3/2 lol

[grim rampart]

how did you get -3/2

[buoyant pine]

i dont even know tbh im just yapping at the end here

idk how to do it

das why i need some help on the last bit

jus to find out a

[grim rampart]

do you know factor theorem

[buoyant pine]

nope

[grim rampart]

do you know algebraic long division

[buoyant pine]

nope

i learnt gcses mysel

[grim rampart]

ok so no point

[buoyant pine]

and a levels myself too rn

[grim rampart]

find videos and practice questions on

factor theorem and algebraic long division

[buoyant pine]

can u not provide help w just this last part pls

i rlly rlly need it

[grim rampart]

ill send you working in a sec

[buoyant pine]

my submission is tomorrow

i dont want to let my professor down

[grim rampart]

but i already know you wont be able to follow it

your prof will be let down more by you having workings that you dont understand

[buoyant pine]

i will revise it but

i just need the guildelines to get there

i will revise it to be able to understand ur working

[grim rampart]

this question is not guidelines

this quesiton is as complicated as it can be

[buoyant pine]

also tysm for helping me

[grim rampart]

this is a terrible question to use as revision

[buoyant pine]

s o like

-3/2

and then -1/5

-1.5

i think

idk

im crying lol this is so difficult

[grim rampart]

THATS WHAT IM SAYING

this is why this is a bad question to revise from

and why having the solution means jack shit

[buoyant pine]

i did like

this

lemme ss

lmk if im right

There’s more work in on other page but that’s what you helped me with.

[grim rampart]

done

thats just the end of the question

[buoyant pine]

so its done?

thats my solution?

[grim rampart]

just submit taht yeah

[buoyant pine]

yaaaaaaaaaayyyy

i finally get itttt

thanks soooo much!!!!

u spent like 1hr just helping me

tysmm

[grim rampart]

nws

[buoyant pine]

are u free tmr i have some complex q on areas i need to do

[grim rampart]

i have no idea when im free

i would very strongly suggest revising easier questions

[buoyant pine]

yeah but unfortunelty like because i have to do a llevel maths in a single year as well as fm

like

i struggle

but