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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

$\begin{aligned} = 4 \int_{0}^{1} (\sqrt{1 - x^{2}}) d x \\ [\int \sqrt{a^{2} - x^{2}} d x = \frac{x \sqrt{a^{2} - x^{2}}}{2} + \frac{a^{2}}{2} \sin^{- 1} (\frac{x}{a})] \\ = 4 \int_{0}^{1} (\sqrt{1^{2} - x^{2}}) d x \\ = 4 {[\frac{x \sqrt{1^{2} - x^{2}}}{2} + \frac{1^{2}}{2} \sin^{- 1} (\frac{x}{1})]}_{0}^{1} \\ = 4 (0 - \frac{π}{4} - 0 - 0) \\ = π sq.units \end{aligned}$

Correct Answer is option B.

Posted by

infoexpert22

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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)

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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