Efficiently Solve a Tricky Double Integral with These Proven Methods

[Batmaniac]

Homework Statement

Evaluate:

<br /> \int_{0}^{4} \int_{\sqrt{x}}^{2}e^y^3dxdy<br />

The Attempt at a Solution

Well that's a Fresnel type function so you can't find an antiderivative for it. I'm pretty sure the point of this assignment isn't Taylor series so I'm quite certain we aren't expected to go down that route.

I tried integrating over x first so my new integral became:

<br /> \int_{0}^{2} \int_{0}^{y^2}e^y^3dydx <br />

(did I do this right?)

which after you integrate the inner integral you obtain:

<br /> \int_{0}^{2}y^2e^y^3<br />

Which is an even more complicated integral.

I also tried converting to polar coordinates but obtained this even more difficult integral:

<br /> \int_{0}^{2\sqrt{10}} \int_{0}^{\frac{\pi}{2}}e^{{r^3}{cos^3\theta}}d\theta{dr}<br />

So any ideas? I tried the two methods we learned in class and the methods which we are supposed to be tested on in this assignment and got nowhere.

 

[Vid]

The integral of y^2*e^(y^3) is a simple substitution.

 

[Batmaniac]

Wow, didn't see that, thanks!