Evaluate the double integral $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { y } ( 3 x + 2 y ) d x d y$ . Round your answer to two decimal places, where applicable.
A)-8.83
B)11.17
C)2.00
D)1.17
E)5.00

Question

Quizplus · Accepted Answer

First, integrate with respect to $x$: $\int_{0}^{y} (3x + 2y) \, dx = \left[\frac{3}{2}x^2 + 2yx\right]_{0}^{y} = \frac{3}{2}y^2 + 2y^2 = \frac{7}{2}y^2$. Then, integrate with respect to $y$: $\int_{0}^{1} \frac{7}{2}y^2 \, dy = \left[\frac{7}{6}y^3\right]_{0}^{1} = \frac{7}{6} \approx 1.17$.

Evaluate the Double Integral ∫01∫0y(3x+2y)dxdy\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { y } ( 3 x + 2 y ) d x d y∫01​∫0y​(3x+2y)dxdy

Evaluate the Double Integral $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { y } ( 3 x + 2 y ) d x d y$