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

Q: The area of the region bounded by the unit circle is:
A. 2π sq units
B. π sq units
C. 3π sq units
D. 4π sq units

Answers (1)

The circle $x^2+y^2=1$

The circle is symmetrical with the x-axis and y-axis

Required Area

$\begin{aligned} & =4 \int_0^1\left(\sqrt{1-x^2}\right) d x \\ & {\left[\int \sqrt{a^2-x^2} d x=\frac{x \sqrt{a^2-x^2}}{2}+\frac{a^2}{2} \sin ^{-1}\left(\frac{x}{a}\right)\right]} \\ & =4 \int_0^1\left(\sqrt{1^2-x^2}\right) d x \\ & =4\left[\frac{x \sqrt{1^2-x^2}}{2}+\frac{1^2}{2} \sin ^{-1}\left(\frac{x}{1}\right)\right]_0^1 \\ & =4\left(0-\frac{\pi}{4}-0-0\right) \\ & =\pi \text { sq.units }\end{aligned}$

Correct Answer is option B.

 

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infoexpert22

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