The area enclosed by the circle x2 + y2 = 2 is equal to:

Question

The area enclosed by the circle $x^{2} + y^{2} = 2$ is equal to:

Smart Achievers · Accepted Answer

(4)

Ans. $2 π$ sq. units

Explanation :

$∵$ $Area = 4 \int_{0}^{\sqrt{2}} \sqrt{2 - x^{2}} d x$

$= 4 {[\frac{x}{2} \sqrt{2 - x^{2}} + \sin^{- 1} (\frac{x}{\sqrt{2}})]}_{0}^{\sqrt{2}}$

$= 4 [0 + \frac{π}{2}]$

$= 2 π sq. units.$

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