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"Integrate f(x, y) = Sqrt(x^2 + y^2) over the region in the x-y plane bounded by the circles r = 1 and r = 4 in the upper half-plane".

Well, I firstly sketched out the region I get as my area in the x-y plane. I deduced that the ranges for x and y are:

0 <= x <= 4

Sqrt[1 - x^2] <= y <= Sqrt[16 - x^2]

1.) Is this right?

2.) How do I then calculate the integral of f(x, y) over this region? I know I'm doing a double integral but I don't see how I can seperate my variables...

Thanks