Region lies inside the circle and to the right of the vertical line

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

Problem

Region

R

lies inside the circle

x^{2}+y^{2}=4

and to the right of the vertical line

x=1

. Which of the following gives the exact area of

R

? (a)

\dfrac{4\pi}{3}+\sqrt{3}

(b)

\dfrac{4\pi}{3}-\sqrt{3}

(c)

2\pi-\sqrt{3}

(d)

\dfrac{4\pi}{3}