Evaluate ∬R xy dA, where R is the region bounded by x^2+y^2≤36, x≥0 and y≥0.

Answer 1

∫[0,6] ∫[0,√(36-x^2)] xy dy dx
∫[0,6] 1/2 xy^2 [0,√(36-x^2)] dx
∫[0,6] 1/2 x (36-x^2) dx
9x^2 - 1/8 x^4 [0,6]
162