Free Area enclosed by polar graphs Practice Problems • Learn To Be

Which expression represents the area of the $\blue{\text{shaded circular segment}}$ inside the circle $\red{r=4\cos\theta}$ and to the left of the line $\purple{r=\sec\theta}$ ?

Choose 1 answer:

A
$\displaystyle 8\int_{0}^{\pi/3} \cos^2\theta\, d\theta + \dfrac12\int_{\pi/3}^{\pi/2} \sec^2\theta\, d\theta$
B
$\displaystyle \dfrac12\int_{0}^{\pi/3} \sec^2\theta\, d\theta + 8\int_{\pi/3}^{\pi/2} \cos^2\theta\, d\theta$
C
$\displaystyle \int_{0}^{\pi/3} \sec^2\theta\, d\theta + 16\int_{\pi/3}^{\pi/2} \cos^2\theta\, d\theta$
D
$\displaystyle 16\int_{0}^{\pi/3} \cos^2\theta\, d\theta + \int_{\pi/3}^{\pi/2} \sec^2\theta\, d\theta$

Area enclosed by polar graphs

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