Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is:

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:

Smart Achievers · Accepted Answer

(1)

Ans. $π$ sq. units

Explanation:

The area bounded by the circle and the lines, $x = 0$ and $x = 2$ , in the first quadrant is represented as shaded region.

$Area O A B = \int_{0}^{2} y d x$

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

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

$= 2 (\frac{π}{2}) = π$

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