Let . Determine the exact area of the region lying above the -axis and between and…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

r>0

. Determine the exact area of the region lying above the

x

-axis and between

x = \dfrac{r}{2}

and

x = r

for the circle

x^{2}+y^{2}=r^{2}

. (a)

r^{2}\left( \dfrac{\pi}{6} + \dfrac{\sqrt{3}}{8} \right)

(b)

\dfrac{\pi r^{2}}{4}

(c)

r^{2}\left( \dfrac{\pi}{6} - \dfrac{\sqrt{3}}{8} \right)

(d)

r^{2}\left( \dfrac{\pi}{3} - \dfrac{\sqrt{3}}{8} \right)