Question

Area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (A)

$\pi$

The area bounded by the circle and the lines, $x=0$ and $x=2$, in the first quadrant is represented as shaded region in the plot.
$\therefore$ Area $OAB={\int }_0^{2}ydx$
$={\int }_0^2\sqrt{4-x^2}dx$
$={[\frac{x}{2}\sqrt{4-x^2}+\frac{4}{2}{\sin }^{-1}\frac{x}{2}]}_0^2$
$=2\left(\frac{\pi }{2}\right)=\pi$sq. units
Thus, the correct answer is A.