Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path C given in polar coordinates is $A = \frac { 1 } { 2 } \int _ { C } r ^ { 2 } d \theta " \text { to find the area of the region }$ bounded by the graphs of the polar equation $r = 15 ( 1 - \cos \theta )$.
A) $\frac { 75 \pi } { 2 }$
B) $\frac { 675 \pi } { 2 }$
C) $\frac { 1125 \pi } { 2 }$
D) $\frac { 45 \pi } { 2 }$
E) $\frac { 15 \pi } { 2 }$

Question

Quizplus · Accepted Answer

The area $A$ of the region bounded by the polar curve $r = 15(1 - \cos\theta)$ can be found using the formula $A = \frac{1}{2}\int_{C} r^2 d\theta$. Substituting $r = 15(1 - \cos\theta)$ into the formula gives $A = \frac{1}{2}\int_{0}^{2\pi} [15(1 - \cos\theta)]^2 d\theta$. Simplifying and integrating yields $A = \frac{675\pi}{2}$.

Use a Computer Algebra System and the Result "The Area A=12∫Cr2dθ" to find the area of the region A = \frac { 1 } { 2 } \int _ { C } r ^ { 2 } d \theta " \text { to find the area of the region }A=21​∫C​r2dθ" to find the area of the region

Use a Computer Algebra System and the Result "The Area $A = \frac { 1 } { 2 } \int _ { C } r ^ { 2 } d \theta " \text { to find the area of the region }$