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  • Provide solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 34

Provide solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 34

Answers (1)

Answer:

 (d)

Hint:

 Area of the circle = 4 X (Area of circle in first quadrant)

Given:

 x2 + y2 = 2

Explanation:

\begin{aligned} &x^{2}+y^{2}=2\\ &y^{2}=2-x^{2} \qquad \qquad \qquad \left [ r^{2}=2\Rightarrow r=\sqrt{2} \right ]\\ &y=\sqrt{2-x^{2}} \end{aligned}

 Area of the circle = 4 X (Area of OAB)

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

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Gurleen Kaur

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