Question

Find the integral of x2 dx dy. Use inner limits = 0 to 2y and outer limits = 0 to 2. (5 points)

Answer 1

$$\displaystyle\int_{0}^{2}\displaystyle\int_{0}^{2y}x^2dxdy=\displaystyle\int_{0}^2[\dfrac{x^3}{3}]\begin{matrix} 2y \\ 0 \end{matrix}dy$$

$$=\displaystyle\int_{0}^2\dfrac{8y^3}{3}dy=[\dfrac{2y^4}{3}]\begin{matrix} 2 \\ 0 \end{matrix}=\dfrac{32}{3}$$