some problems by integrating by parts

[bright hearth]

is this correct?

[digital relic]

$$ /int sin(2y)y /dd y$$

[bright hearth]

wjat

[digital relic]

I don’t know how to make it work, right

I’m checking

[bright hearth]

nah, just tell me the result

dont loose time in that crappy thing

[digital relic]

Well, I’m trying to confirm what the question is I don’t know what you wrote down

[bright hearth]

let me fix it a little

[bright hearth]

maybe like this

i want to know if the u*v thing is right

Im having troubles with that

[digital relic]

Well, you wrote down the equation correctly for the substitutions but when you did it, it’s wrong because you put ysin(2y) when its -cos(2y

Also, you integrated sin(2y wrong

[bright hearth]

you right

exaclty

thanks

[bright hearth]

so what i do now with the left thing?

is all remaining in y * cos - all the barrus thing?

[digital relic]

You still did it wrong

[bright hearth]

what's wrong now

[digital relic]

When you look at the bottom you still need to integrate and you multiply by 1/2 again

[bright hearth]

from where did you take the /2 thing?

[digital relic]

Because of the 2y inside the sin

Because you integrate it

[bright hearth]

what

okay

can u tell me the theory?

of that

[digital relic]

Its the opposite of chain rule

[bright hearth]

is thos?

1/a = constant

[digital relic]

Yes

[bright hearth]

nice

buddy

does the

integral u' * cos u = sen u

equal for sen?

[digital relic]

?

Do you mean sin?

[bright hearth]

like u'* sen u = -cos u

yes

sorry

sen is for spanish people

sorry

[digital relic]

Ok

[bright hearth]

but is that possibpe?

u' * sin u = - cos u

[digital relic]

If f(x)=sin u
Then f’(x)=cos u

But integration is the opposite

[bright hearth]

soo

why is the property

u' * cos u = sen u

[digital relic]

Wdym

[bright hearth]

what means wdym?

[digital relic]

“What do you mean”

[bright hearth]

there is a property

in integration

that means

if u have integral of u' * cos u = sin u

like

the

u' * u = u ^ n+1 / n+1

[digital relic]

So you’re using u’ as a integral sign?

[bright hearth]

no

u' means the derivade

[digital relic]

Well, that property isn’t true. I don’t know where you got it from.

[bright hearth]

what obne

one

[digital relic]

That

[bright hearth]

bro

literally

all the teachers sais it

im 1 degree engineering

i dont think they wrong

even my teacher for extra school

sais it

[digital relic]

I think you’re misunderstanding what they said

[bright hearth]

if the derivade is appearing multiplaying the element, the result is the element elevated n + 1 and divided by n + 1

so

what is

[bright hearth]

that right

[digital relic]

OK, well that’s not what I thought you meant

[bright hearth]

im pooping my self

wtf

[digital relic]

Anyway, what do you need now ?

[bright hearth]

i need to know

why that isnt x^3 /3

and is that

[digital relic]

It’s because it already has dx

[bright hearth]

oh

in that case

can i multiply 2x * x2?

like all the life?

[digital relic]

?

[bright hearth]

must be done by parts?

[digital relic]

It doesn’t have to be done by parts

It’s just when you’re integrating you automatically put in the dx

[bright hearth]

but it will be in the case i told u x^3 /3

[bright hearth]

what

i dot get u

[digital relic]

Are you talking about a new integral or the same one?

[bright hearth]

the same one

[digital relic]

Then no

[bright hearth]

how would be

2x * x^2 = x^3 /3

?

[digital relic]

Because it’s put in there automatically, there would be different rules if it wasnt

[digital relic]

It doesn’t

[bright hearth]

soo

the thing i explained

of the derivate of a thing multiplaying

is the thing elevated n+1 and divided by n +1

[digital relic]

After you integrate

Do you understand?

[bright hearth]

no

i do not underestand

i dont know what we talking about

i have exam the thuesday

[digital relic]

What are you confused on?

[bright hearth]

and i discovered that the only thing i knew

is wrong

why

[digital relic]

No

[bright hearth]

2x * x^2 isnt x^3 /3

why

when you sayed

not what calculator sais

[digital relic]

Would it be easier if we got on a voice call so I could quickly explain it to you?

[bright hearth]

let my grab my ear thing

u underestand

[digital relic]

Ok

[bright hearth]

ready

when u tell me

[digital relic]

I sent you the voice call

Is it working?

@bright hearth just tell me what you are saying in chat

Do you understand now?

[bright hearth]

i was meaning that so the calculator is doing like 2 times the derivaded

i underestood

so property is right, but not in the calculator

[digital relic]

Yes because du=u’

[bright hearth]

nice soo, becaus i was getting crazy thinking i was gonna fail

thanks a lot

[digital relic]

Do you understand what integration does?

[bright hearth]

yes

i do

[digital relic]

So can you solve the original problem now?

[bright hearth]

yes

[digital relic]

$$ \int sin(2y)y \dd y$$

[pulsar thorn]

Loukes1315

[digital relic]

So do you know what this integrates to?

Or how to integrate it?

[bright hearth]

yes

but i get one last doubt

when i do the u *v thing

all the derivate by parts

[digital relic]

Yeah?

[bright hearth]

the sarrus thing of -4 and -12

is applaying to all the ecaution?

[digital relic]

Yes

[bright hearth]

so i will do

[digital relic]

Integrate the second part

[bright hearth]

do you mean this?

in the case that a woudl be that ( never ) , i must do a in -4 - a in -12

[bright hearth]

omw

alry

is that

i had -cos ( 2y)/ 2

[digital relic]

$$ \frac{1}{8} [ \frac{y}{2} (-cos(2y)- \frac{1}{2} \int -cos(2y) \dd y $$

[bright hearth]

i have that

literally

wait stoo

stop

[digital relic]

Now integrate the second part

[bright hearth]

wrong

[digital relic]

?

[bright hearth]

second part is -cos (2y) /2

so we integrate

i got -sin 2y

/2

[digital relic]

Ok

[pulsar thorn]

Loukes1315

[digital relic]

I made a mistake but you integrated wrong

Do you remember what the integral of cos(ax)dx=?

[bright hearth]

i have this

yes

-sen 2y /2

is done right

[digital relic]

Well you didn’t account for the chain rule

[bright hearth]

what

so

[digital relic]

For cos(2y

You need to multiply by 1/2 again

[bright hearth]

you got it wrong, that isnt hte integral to do

that 1/2

is when i already integrate

and got -sin 2y

wait

u true

the integral of - cos 2y = sen 2y /2

[digital relic]

Yes

[bright hearth]

this is so

is the -4 and - 12 righ?

so i must do first with -4 , rest it to the -12?

[digital relic]

So if this new equation is F(y) you are calculating F(-4)-F(-12)

[bright hearth]

nice

so because this was a bit like complicated, could you check if all that came from this

[digital relic]

Yes it does

[bright hearth]

im gonna cry

of happines

i prommise

[digital relic]

Now you just have to calculate

[bright hearth]

-0,413751

im farting right now

[digital relic]

Uh

How did you get that

[bright hearth]

is right

i put it in the calculatir

LETS GOO

i dont know

[digital relic]

Um

[bright hearth]

wont ask anyone

[digital relic]

Can I see the calculation?

[bright hearth]

that is -0,413726033

and i got tht

[digital relic]

Oh yeah, I just put something wrong into my calculator

[bright hearth]

want to know why the result is so ugly?

because i did the definition wrong

[digital relic]

Wdym

[bright hearth]

yes

this is related to this exercise

[bright hearth]

can i apply 2a to get the area?

or i must do the 4 integrals possible

[digital relic]

Wdym

[bright hearth]

i mean, i can do 2*a and do only 2 intergals

for calculate

I can do the area by similarity

[digital relic]

What is your question?

[bright hearth]

if i can do that

i calculate one part

and multiply per 2

[digital relic]

If its a even function

[bright hearth]

what

[digital relic]

If it’s the same on both sides of the Y axis

[bright hearth]

so i can do one side

and multiply by 2?

[digital relic]

Sometimes it depends. What’s the function

[bright hearth]

what fuctions do limit me?

[digital relic]

?

[bright hearth]

what fuctions doesnt allow me to do that?

[digital relic]

Anything that isn’t even

[bright hearth]

i translated to spanish

dont underestand

[digital relic]

The blue function is an even function and the red one is an odd one

Do you see how the red one isn’t the same on both sides of the y axis?

[bright hearth]

so cos

is simetric

sin isnt

[digital relic]

Yes

[bright hearth]

so i can do it

and multiply by 2

[digital relic]

Yes

[bright hearth]

nice

[flat hearth]

.solved