Evaluate the iterated integral $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 2 } ( x + y ) d x d y$ .
A) $\frac { 1 } { 2 }$

B)2

C) $\frac { 3 } { 2 }$

D)2.
E) $\frac { 5 } { 2 }$
F)3
G) $\frac { 7 } { 2 }$

H)4

Question

Evaluate the iterated integral $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 2 } ( x + y ) d x d y$ .
A) $\frac { 1 } { 2 }$

B)2

C) $\frac { 3 } { 2 }$

D)2.
E) $\frac { 5 } { 2 }$
F)3
G) $\frac { 7 } { 2 }$

H)4

Quizplus · Accepted Answer

First, integrate with respect to $x$: $\int_{0}^{2} (x+y) \, dx = \left[\frac{x^2}{2} + xy\right]_{0}^{2} = \frac{4}{2} + 2y = 2 + 2y$. Then, integrate with respect to $y$: $\int_{0}^{1} (2 + 2y) \, dy = \left[2y + y^2\right]_{0}^{1} = 2 + 1 = 3$.

Evaluate the Iterated Integral ∫01∫02(x+y)dxdy\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 2 } ( x + y ) d x d y∫01​∫02​(x+y)dxdy

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