What to do with the e^(y^3)? I dont know how to integrate it.

[Tadhg90]

Homework Statement

Evaluate the following integral by first reversing the order of integration

ZZR x^3 e^(y^3) dxdy

The first integral is from 3 to 0 and the inner integral is from 9 to x^2

Homework Equations

The Attempt at a Solution

i know how to revers the order its just changing dydx to dxdy
and x^3 is just x^4/4 but i don't know what to do with the e^(y^3)

 

[Mark44]

Homework Statement

Evaluate the following integral by first reversing the order of integration

ZZR x^3 e^(y^3) dxdy

ZZR? What is that?

The first integral is from 3 to 0 and the inner integral is from 9 to x^2

Do you mean from 0 to 3 and from x^2 to 9? The usual practice is to state the lower limits of integration first.

Homework Equations

The Attempt at a Solution

i know how to revers the order its just changing dydx to dxdy

There's more to it than that. You need to change the limits of integration. To do that, it's helpful to sketch the region over which integration is taking place.

and x^3 is just x^4/4 but i don't know what to do with the e^(y^3)

 

[Tadhg90]

ZZ is the double integral i copy pasted from adobe reader, R is just the values from 0 to 3 and from x^2 to 9 [yes i meant this way]

 

[Mark44]

R stands for "region" - the region in the plane over which integration is taking place.

Do you know what this region looks like?

 

[SammyS]

Homework Statement

Evaluate the following integral by first reversing the order of integration

ZZR x^3 e^(y^3) dxdy

The first integral is from 3 to 0 and the inner integral is from 9 to x^2

Homework Equations

The Attempt at a Solution

i know how to revers the order its just changing dydx to dxdy
and x^3 is just x^4/4 but i don't know what to do with the e^{y^3)

I suspect your integral is: $$\displaystyle \int_0^{\,3}\int_{x^2}^{\,9} x^3 e^{y^3}\ dy\ dx$$

 

[Tadhg90]

yes that's the integral. but what is the integral of e^(y^3)? I am guessing than with respect to it doesn't change because of the x^3 beside it, i mean its not a constant to it, and then integrating it with respect to y would it be 3y^2 * e^(y^3). this is just a guess but i bont know if its right...

 

[Mark44]

yes that's the integral. but what is the integral of e^(y^3)? I am guessing than with respect to it doesn't change because of the x^3 beside it, i mean its not a constant to it, and then integrating it with respect to y would it be 3y^2 * e^(y^3). this is just a guess but i bont know if its right...

That's not the integral you need to do, and most likely is not possible to do. That's the reason they're asking you to reverse the order of integration.

I asked in post #4, do you know what the region of integration looks like? You will need to know this in order to reverse the order of integration.

 

[Tadhg90]

sorry, i didnt see that, eh no the R is nothing acctualy it was in the adobe example i tried to copy on here. in the problem it only says "Evaluate the following integral by first reversing the order of integration" it looks like what Sammys posted on post #5 except its dxdy like u just pointed out.

 

[Mark44]

I suspect your integral is: $$\displaystyle \int_0^{\,3}\int_{x^2}^{\,9} x^3 e^{y^3}\ dy\ dx$$

sorry, i didnt see that, eh no the R is nothing acctualy it was in the adobe example i tried to copy on here. in the problem it only says "Evaluate the following integral by first reversing the order of integration" it looks like what Sammys posted on post #5 except its dxdy like u just pointed out.

Now I'm confused. The integral that Sammy wrote looks like what you described in your first post. With the limits of integration he shows, the correct order would by dy then dx.

If that's not how the integral is shown in your book, please scan the page and post it here.

Also, I have asked twice whether you know what the region of integration looks like? Do you?

 

[HallsofIvy]

I agree with Mark44- the integral, as you give it, makes no sense. You cannot integrate, with respect to x, from $x^2$ to 9.

$$\int_{x=0}^3\int_{y= x^2}^9 x^3e^{y^3}dydx$$
can be integrated by changing the order of integration- but that is NOT "just changing dydx to dxdy". You have to also change the limits of integration. That is why Mark44 is asking you repeatedly if you know what the region looks like. That's the first step in changing the limits of integration.