Determine the integral

Question

Determine the integral of x y dx dy. Use inner limits=0 to (y + 1) and outer limits=0 to 1.

Answer 1

∫₀¹y∫₀^y+1xdx = 1/2∫₀¹yx²₀^y+1dy = 1/2∫₀¹y(y + 1)²dy = 1/2∫₀¹(y³ + 2y² + y)dy = 1/2(y⁴/4 + 2y³/3 + y²/2)₀¹ =

1/2(1/4 + 2/3 + 1/2) = 17/24