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  • Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 32 maths

Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 32 maths

Answers (1)

Answer:

 (a)

Hint:

 Integration

Given:

 x2 + y2 = 4 and x = 0, x = 2

Explanation:

x^{2}+y^{2}=4\Rightarrow y=\sqrt{4-x^{2}}

Area OAB,

\begin{aligned} &=\int_{0}^{2}\sqrt{4-x^{2}}dx\\ &=\left [ \frac{x}{2}\sqrt{4-x^{2}}+\frac{4}{2}sin^{-1}\frac{x}{2} \right ]_{0}^{2}\\ &=\frac{2}{2}\sqrt{4-4}+2sin^{-1}\frac{2}{2}-0-2sin^{-1}0\\ &=2sin^{-1}1\\ &=2\left ( \frac{\pi }{2} \right )\\ &=\pi \end{aligned}

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Gurleen Kaur

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