Hitunglah \( \displaystyle \int_1^2 \int_2^4 \ (x+2y) \ dx \ dy \).
Pembahasan:
\begin{aligned} \int_1^2 \int_2^4 \ (x+2y) \ dx \ dy &= \int_1^2 \ \left[ \frac{1}{2}x^2+2xy \right]_2^4 \ dy \\[8pt] &= \int_1^2 \ \left[ (8+8y)-(2+4y) \right] \ dy \\[8pt] &= \int_1^2 \ (6+4y) \ dy = \left[ 6y+2y^2 \right]_1^2 \\[8pt] &= (12+8)-(6+2) \\[8pt] &= 12 \end{aligned}