By Fubini's Theorem, the double integral $\iint$R $4 x e ^ { y } d A$ with $R = \{ ( x , y ) : 0 \leq x \leq 1,0 \leq y \leq 1 \}$ is

A) $e - 1$
B) $e + 1$
C) $2 ( e - 1 )$
D) $2 ( e + 1 )$
E) $e + 2$

Question

By Fubini's Theorem, the double integral $\iint$R $4 x e ^ { y } d A$ with $R = \{ ( x , y ) : 0 \leq x \leq 1,0 \leq y \leq 1 \}$ is

A) $e - 1$
B) $e + 1$
C) $2 ( e - 1 )$
D) $2 ( e + 1 )$
E) $e + 2$

Quizplus · Accepted Answer

To evaluate the double integral using Fubini's Theorem, we first integrate with respect to $y$ from 0 to 1, and then with respect to $x$ from 0 to 1. The integral becomes $\int_0^1 \int_0^1 4x e^y \, dy \, dx$. The inner integral with respect to $y$ is $\int_0^1 e^y \, dy = e - 1$. Thus, the integral becomes $\int_0^1 4x(e - 1) \, dx = 2(e - 1)$.

By Fubini's Theorem, the Double Integral ∬\iint∬ R 4xeydA4 x e ^ { y } d A4xeydA

By Fubini's Theorem, the Double Integral $\iint$ R $4 x e ^ { y } d A$