Integrate the function f over the given region.
-$f ( x , y ) = \sin 11 x$ over the rectangle $0 \leq x \leq \frac { \pi } { 11 } , 0 \leq y \leq \pi$
A) $\frac { 2 \pi } { 11 }$
B) $\frac { \pi } { 22 }$
C) $\pi$
D) $\frac { \pi } { 11 }$

Question

Quizplus · Accepted Answer

The integral of $f(x, y) = \sin 11x$ over the given rectangle can be computed by integrating with respect to $x$ from $0$ to $\frac{\pi}{11}$ and with respect to $y$ from $0$ to $\pi$. The integral with respect to $x$ gives $\frac{1}{11}[-\cos 11x]_0^{\frac{\pi}{11}} = \frac{2}{11}$, since $\cos(\pi) = -1$ and $\cos(0) = 1$. The integral with respect to $y$ is simply $y$ evaluated from $0$ to $\pi$, which gives $\pi$. Multiplying these results gives $\frac{2}{11} \times \pi = \frac{2\pi}{11}$.

Integrate the Function F Over the Given Region f(x,y)=sin⁡11xf ( x , y ) = \sin 11 xf(x,y)=sin11x

Integrate the Function F Over the Given Region $f ( x , y ) = \sin 11 x$