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  • Please solve RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 41 maths textbook solution

Please solve RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 41 maths textbook solution

Answers (1)

Answer:

 (a)

Hint:

 Find the graph between y2 = x and 2y = x

Given:

 y2 = x and 2y = x

Explanation:

Intersection point,

\begin{aligned} &y=\frac{x}{2}\\ &y^{2}=x\\ &\left ( \frac{x}{2} \right )^{2}=x\Rightarrow \frac{x^{2}}{4}=x\\ &x^{2}-4x=0\\ &x(x-4)=0\\ &x=0,x=4 \end{aligned}

Area of the bounded region ABC

\begin{aligned} &=\int_{0}^{4}\left ( \sqrt{x}-\frac{x}{2} \right )dx\\ &=\left [ \frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{2}}{4} \right ]_{0}^{4}\\ &=\frac{2}{3}(4)^\frac{3}{2}-\frac{(4)^{2}}{4}\\ &=\frac{4}{3} \text { sq.units } \end{aligned}

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Gurleen Kaur

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