I’m teaching double integrals, and there was this really great problem:
over the region .
The problem is supposed to show that changing the order of integration can make the problem really easy or really hard.
is easy to solve.
is hard to solve.
However, I don’t think the second integral should be impossible to solve. It’s been so long since I’ve really dug into integration, and we tried in class and couldn’t find a quick way to solve the second integral. Any ideas?
For those who know calculus but not Multivariable Calculus, the hard part of the second integral is simply being asked to solve: , where is simply a constant.