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  • The area of the region bounded by the circle x^2 + y^2 = 1 is A. 2π sq units

The area of the region bounded by the circle x^{}2 + y^{}2 = 1 is
A. 2π sq units
B. π sq units
C. 3π sq units
D. 4π sq units

Answers (1)

B)

The circle x^{}2 + y^{}2 = 1

The circle is symmetrical with the x axis and y axis

Required Area

\\ =4 \int_{0}^{1}\left(\sqrt{1-x^{2}}\right) d x \\ {\left[\int \sqrt{a^{2}-x^{2}} d x=\frac{x \sqrt{a^{2}-x^{2}}}{2}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x}{a}\right)\right]} \\ =4 \int_{0}^{1}\left(\sqrt{1^{2}-x^{2}}\right) d x \\ =4\left[\frac{x \sqrt{1^{2}-x^{2}}}{2}+\frac{1^{2}}{2} \sin ^{-1}\left(\frac{x}{1}\right)\right]_{0}^{1} \\ =4\left(0-\frac{\pi}{4}-0-0\right) \\ =\pi \text { sq.units }

 

 

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infoexpert22

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