Evaluate the double integral over the given region.
-$$\iint _ { R } \sin 11 x d A , R : 0 \leq x \leq \frac { \pi } { 11 } , 0 \leq y \leq \pi$$
A) $\frac { 2 \pi } { 11 }$
B) $\frac { \pi } { 11 }$
C) $\pi$
D) $\frac { \pi } { 22 }$

Question

Quizplus · Accepted Answer

The integral can be separated into two integrals due to the independence of $x$ and $y$. The integral over $x$ is $\int_0^{\frac{\pi}{11}} \sin(11x) dx$, which evaluates to $\frac{1}{11}[-\cos(11x)]_0^{\frac{\pi}{11}} = \frac{2}{11}$. The integral over $y$ is $\int_0^{\pi} dy = \pi$. Multiplying these results gives $\frac{2}{11} \times \pi = \frac{2\pi}{11}$.

Evaluate the Double Integral Over the Given Region ∬Rsin⁡11xdA,R:0≤x≤π11,0≤y≤π\iint _ { R } \sin 11 x d A , R : 0 \leq x \leq \frac { \pi } { 11 } , 0 \leq y \leq \pi∬R​sin11xdA,R:0≤x≤11π​,0≤y≤π

Evaluate the Double Integral Over the Given Region $\iint _ { R } \sin 11 x d A , R : 0 \leq x \leq \frac { \pi } { 11 } , 0 \leq y \leq \pi$