Question

The area bounded by the curve $x^2+y^2=1$ in first quadrant is

• A. $\frac{\pi }{4}$ sq. units
• B. $\frac{\pi }{2}$ sq. units
• C. $\frac{\pi }{3}$ sq. units
• D. $\frac{\pi }{6}$ sq. units

Answer 1

Answer: (A)

We have, $x^2+y^2=1$, a circle with centre $(0,0)$ and radius = 1.

Required area = area of shaded region
$=\underset{0}{\overset{1}{\int }}\sqrt{1-x^2}dx={\left[\frac{x}{2}\sqrt{1-x^2}+\frac{1}{2}si{n}^{-1}\frac{x}{1}\right]}_0^1$
$=\left[\frac{1}{2}si{n}^{-1}1\right]=\left(\frac{1}{2}\times \frac{\pi }{2}\right)=\frac{\pi }{4}$ Sq. units