Evaluate the double integral over the given region.
-$\iint _ { R } e ^ { 2 x + 3 y } d A , R : 0 \leq x \leq 1,0 \leq y \leq 1$
A) $\frac { 1 } { 6 } \left( e ^ { 5 } - e ^ { 3 } - e ^ { 2 } + 1 \right)$
B) $\frac { 1 } { 6 } \left( e ^ { 5 } - \mathrm { e } ^ { 3 } - \mathrm { e } ^ { 2 } - 1 \right)$
C) $\frac { 1 } { 4 } \left( e ^ { 5 } - e ^ { 3 } - e ^ { 2 } - 1 \right)$
D) $\frac { 1 } { 4 } \left( e ^ { 5 } - \mathrm { e } ^ { 3 } - \mathrm { e } ^ { 2 } + 1 \right)$

Question

Quizplus · Accepted Answer

Evaluate the integral by directly integrating over the given region:
$$\int_0^1\int_0^1 e^{2x+3y} dydx = \int_0^1 \left[\frac{e^{2x+3y}}{3}\right]_0^1 dx = \int_0^1 \frac{e^{2x+3}-e^{2x}}{3} dx = \left[\frac{e^{2x+3}}{6}-\frac{e^{2x}}{6}\right]_0^1=\frac{1}{6}(e^5-e^3-e^2+1)$$Therefore, the answer is choice A.

Evaluate the Double Integral Over the Given Region ∬Re2x+3ydA,R:0≤x≤1,0≤y≤1\iint _ { R } e ^ { 2 x + 3 y } d A , R : 0 \leq x \leq 1,0 \leq y \leq 1∬R​e2x+3ydA,R:0≤x≤1,0≤y≤1

Evaluate the Double Integral Over the Given Region $\iint _ { R } e ^ { 2 x + 3 y } d A , R : 0 \leq x \leq 1,0 \leq y \leq 1$