Double integral help

[scottj19x89]

Having a hard time understanding how to do this:

[integral from 0 to a][integral from 0 to b] e^(MAX(b^2x^2, a^2y^2)) dy dx

someone said to do the inside integral first, but I'm confused as to how that works because b and y aren't together in the MAX part

thanks in advance

 

[tkhunny]

Whoever said to do the inside integral first doesn't seem to have looked at the actual problem statement. Of course the inside one would go first, but that is just not the difficulty with this integral. The difficulty is the MAX function!

You're going to have to split things up.

You've a rectangle with opposite endpoints (0,0) and (a,b).

You must reconcile the integral in various parts of the Domain.

The diagonal of the rectangle is important, ay = bx.

Let's see what you get. It will take two entirely different integrals.