Answer to Question #148918 in Calculus for Water

Question

Evaluate ∫∫D xydA, where D is the region bounded by x = y^3 and y = x^2.

Answer 1

$\int\int _D xy dA= \int ^1_0\int ^{y=x^{\frac{1}{3}}}_{y=x^2} xy dydx= \int^1_0 x ( \frac{x^{\frac{2}{3}}-x^4}{2}) dx\\ =\int ^1_0 \frac{(x^{\frac{5}{3}}-x^{5})}{2}dx\\ =\frac{5}{48}$