Hitunglah \( \displaystyle \int_0^2 \int_0^1 \ (x^2+2y) \ dx \ dy \).
Pembahasan:
Dengan menggunakan aturan pengintegralan, kita peroleh hasil berikut:
\begin{aligned} \int_0^2 \int_0^1 \ (x^2+2y) \ dx \ dy &= \int_0^2 \ \left[ \frac{1}{3}x^3+2xy \right]_0^1 \ dy \\[8pt] &= \int_0^2 \ \left[ \left( \frac{1}{3}+2y \right)-0 \right] \ dy \\[8pt] &= \int_0^2 \ \left( \frac{1}{3}+2y \right) \ dy \\[8pt] &= \left[ \frac{1}{3}y+y^2 \right]_0^2 = \left( \frac{2}{3}+4 \right)-0 \\[8pt] &= \frac{14}{3} \end{aligned}