Find the area of the region bounded by $x = 1 + \sin t , y = \sin t , 0 \leq t \leq \pi$ , and the x-axis.
A) $4 \pi$
B) $\frac { 3 \pi } { 2 }$
C) $2 \pi$
D) $\frac { \pi } { 4 }$
E) $\frac { \pi } { 2 }$
F) $\frac { \pi } { 6 }$
G) $\pi$
H) $\frac { \pi } { 3 }$

Question

Find the area of the region bounded by $x = 1 + \sin t , y = \sin t , 0 \leq t \leq \pi$ , and the x-axis.
A) $4 \pi$ 
B) $\frac { 3 \pi } { 2 }$ 
C) $2 \pi$ 
D) $\frac { \pi } { 4 }$ 
E) $\frac { \pi } { 2 }$ 
F) $\frac { \pi } { 6 }$ 
G) $\pi$ 
H) $\frac { \pi } { 3 }$

Quizplus · Accepted Answer

The area can be found by integrating the function $y = \sin t$ with respect to $x = 1 + \sin t$. The limits of integration for $t$ are from 0 to $\pi$. The integral of $\sin t$ from 0 to $\pi$ is 2, and the width of the region is 1, giving an area of $\frac{\pi}{2}$.

Find the Area of the Region Bounded By x=1+sin⁡t,y=sin⁡t,0≤t≤πx = 1 + \sin t , y = \sin t , 0 \leq t \leq \pix=1+sint,y=sint,0≤t≤π

Find the Area of the Region Bounded By $x = 1 + \sin t , y = \sin t , 0 \leq t \leq \pi$