Evaluating a Reversed Order Double Integral

[unreal89]

Homework Statement

Eveluate by reversing order of integration

$$\int^{2}_{0}\int^{1}_{y/2} ye^{x^3}dxdy$$

Homework Equations

The Attempt at a Solution

this is what I got...

$$\int^{1}_{0}\int^{2x}_{0} ye^{x^3}dydx$$

I end up with...

$$\int^{1}_{0} 2x^2e^{x^3}dx$$

I don't know how to integrate this... any tips? thanks

 

[lanedance]

almost there - try a substitution

 

[unreal89]

I'm sorry for being so slow... But I'm not sure what to substitute? Thanks

 

[gabbagabbahey]

I'm sorry for being so slow... But I'm not sure what to substitute? Thanks

Well, you probably know how to integrate $e^u du$, so maybe try the substitution $u=x^3$ and see what happens.