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is this double integral setup right? f(x,y) = kxy , x>=0, y>= 0 , 20 <= x + y <= 30

So f(x,y) = kxy, it's a joint probability density function and I must find k so that the integral over the valid range is 1.

My multivariate calculus is a little rusty and my first attempt which looked like (attached) yielded a k of -0.0012 and an integral of 1.

However I solved for k by double integrating with the calculator and setting the to 1 so of course it will yield 1 for the given interval, what I want to confirm is that the integral was setup properly.

thanks!

Attachment 20066