Definite Integrals

[brazen bane]

Is it possible to find a new set of limits of integration of a definite integral after finding the area under a curve and the function?

Number 2 letter b

[coral acorn]

Int(k,0) ydx = int(✓6,k) ydx
you take intervals [k,0] and [✓6,k]

@brazen bane

[brazen bane]

ok idk what to do to find k

[coral acorn]

$\int_0^k\ f(x)\ dx\ = \int_k^{root 6} \ f(x)\ dx$

[hearty dirge]

visionaryM

[coral acorn]

@brazen bane solve for this

[brazen bane]

yeah i know that but idk how

@coral acorn

[coral acorn]

Do You know substitution method???

@brazen bane

[brazen bane]

where does the 2x come from in the numerator

[coral acorn]

x is already given
I multiply 2 both sides

[brazen bane]

why did u multiply both sides by 2

[coral acorn]

To use the substitution rule of integration

[coral acorn]

And multiplying both sides by same number doesn't change the equation

[brazen bane]

ok idk that rule then

is there another way to do this?

[coral acorn]

Nah

[brazen bane]

bro what

ok thanks theb

then

[coral acorn]

No this is the only way if you are dealing with integration you should learn substitution property otherwise you're doomed

[brazen bane]

my teacher hasnt taught us it yet tho :|

[coral acorn]

Then complain about him/her because for integration this property is very important

[brazen bane]

ok can u help me with something else

[coral acorn]

What is it???

[brazen bane]

number 5

i drew the graph and i know that it is a volume by washers

but the graph when y is between 0 to 1 only has one function
our teacher told us that its the volume of the outside washer minus the inside washer

so from 0 to 1 there is only one function so there is no outside or inside

[coral acorn]

Show me the solution

[brazen bane]

but from 1 to 4 there is an outside and inside function

idk if u can see that well

[coral acorn]

What about -1 to 0???

[brazen bane]

a solid is formed by revolving around x=-1

but when y is between 0 and 1 there is only one function

[coral acorn]

@brazen bane

[brazen bane]

yeh and it revolves around x=-1 and forms a solid