Evaluate the integral ∬𝐷(𝑥2−𝑦2)𝑑𝐴 where 𝐷 is the region in the first quadrant between the circles of radius 4 and radius 7.

Question

∫Evaluate the integral ∫∫_D(x²-y²)dA where D is the region in the first quadrant between the circles of radius 4 and radius 7.

Answer 1

f(y, x) = - f(x, y) and (x,y) ∈ D iff (y, x) ∈ D since D is the region between circles of radius 4 and 7 in the first quadrant. Therefore the integral is 0.