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  • Provide solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 30

Provide solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 30

Answers (1)

Answer:

 (b)

Hint:

 Integration

Given:

 x2 + y2 = 4 and x + y = 2

Explanation:

x2 + y2 = 4

r = 2

Area OAB,

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

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Gurleen Kaur

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