Double Integral over General Region : Hass Section 13.2 - Problem 5

[atrain77abc]

Homework Statement

Outer Integral: From zero to one dy
Inner Integral: from zero to y^2 dx

Function is: 3y^3 * e^(xy)

Homework Equations

None

The Attempt at a Solution

Have tried numerous u substitutions on e^(xy), but taking me nowhere. I am clearly doing something wrong. Assuming 3y^3 is a constant and does not need to be integrated when integrated with respect to x.

Solutions manual shows result of inner integral being [3y^2 * e^(xy)] from zero to y^2 - which appears to me that a y in the original 3y^3 simply disappeared! No idea how they are getting from 3y^3 to 3y^2 as the result of the first integration!

I am quite sure this is an easy problem and I am simply overlooking a very simple step.

 

[fzero]

You need to use integration by parts.