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Q.
The area bounded by the curve $x^{2} + y^{2} = 1$ in first quadrant is
Application of Integrals
Solution:
We have, $x^{2} + y^{2} = 1$, a circle with centre $(0,0)$ and radius = 1.
Required area = area of shaded region
$=\int\limits_{0}^{1}\sqrt{1-x^{2}} \, dx=\left[\frac{x}{2}\sqrt{1-x^{2}}+\frac{1}{2}sin^{-1}\frac{x}{1}\right]_{0}^{1}$
$=\left[\frac{1}{2}sin^{-1}1\right]=\left(\frac{1}{2}\times\frac{\pi}{2}\right)=\frac{\pi}{4}$ Sq. units
