Question

double integrate x^2 y dA , R is the region in quadrants 1 and 4 bounded by the semicircle of radius 4 centered at (0,0)

Answer 1

Keep in mind that the equation for a circle centered at (0, 0) with radius 4 is \(x^2 + y^2 = 4^2 = 16\). You should be able to use this to set your integration bounds on each integral so that you can integrate properly.