By Fubini's Theorem, the double integral $\iint$R $2 x \tan ( y ) d A$ with $R = \left\{ ( x , y ) : 0 \leq x \leq 1,0 \leq y \leq \frac { \pi } { 4 } \right\}$ is

A) $\frac { \ln 3 } { 2 }$
B) $\frac { \ln 2 } { 2 }$
C) $\frac { \ln 2 } { 4 }$
D) $\frac { \ln 2 } { 3 }$
E) $\frac { \ln 3 } { 4 }$

Question

By Fubini's Theorem, the double integral $\iint$R $2 x \tan ( y ) d A$ with $R = \left\{ ( x , y ) : 0 \leq x \leq 1,0 \leq y \leq \frac { \pi } { 4 } \right\}$ is

A) $\frac { \ln 3 } { 2 }$
B) $\frac { \ln 2 } { 2 }$
C) $\frac { \ln 2 } { 4 }$
D) $\frac { \ln 2 } { 3 }$
E) $\frac { \ln 3 } { 4 }$

Quizplus · Accepted Answer

The integral can be evaluated by integrating with respect to $x$ first, giving $\int_0^1 2x \, dx = 1$. Then integrate with respect to $y$, $\int_0^{\pi/4} \tan(y) \, dy = \ln(\sec(y))\big|_0^{\pi/4} = \ln(\sqrt{2}) = \frac{\ln(2)}{2}$.

By Fubini's Theorem, the Double Integral ∬\iint∬ R 2xtan⁡(y)dA2 x \tan ( y ) d A2xtan(y)dA

By Fubini's Theorem, the Double Integral $\iint$ R $2 x \tan ( y ) d A$