Evaluate the double integral ∬DxcosydA, where D is bounded by y=0, y=x2, and x=5.

Answer 1

∫∫_DxcosydA = ∫₀⁵xdx∫₀^{x^2}cosydy = ∫₀⁵xsiny₀^{x^2}dx = ∫₀⁵xsinx²dx = -1/2cosx²₀⁵ = 1/2(1 - cos25) = 0.0044