The area of smaller part between the circle x2 + y2 = 4 and the line x = 1 is:

Question

The area of smaller part between the circle $x^{2} + y^{2} = 4$ and the line $x = 1$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{4 π}{3} - \sqrt{3}$ sq. units

Explanation :

$Area of smaller part = 2 \int_{1}^{2} \sqrt{4 - x^{2}} d x$

$= 2 {[\frac{x}{2} \sqrt{4 - x^{2}} + 2 \sin^{- 1} (\frac{x}{2})]}_{1}^{2}$

$= 2 [2 \cdot \frac{π}{2} - (\frac{\sqrt{3}}{2} + 2 \cdot \frac{π}{6})]$

$= 2 [π - (\frac{\sqrt{3}}{2} + \frac{π}{3})] = \frac{4 π}{3} - \sqrt{3} sq. units.$

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