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  • Please solve RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 33 maths textbook solution

Please solve RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 33 maths textbook solution

Answers (1)

Answer:

 (b)

Hint:

 Integration

Given:

 y2 =4x, y-axis (x = 0) and y=3

Explanation:

\begin{aligned} &x=0\\ &y^{2}=4(0)=0\\ &y=0 \text { and } y=3\\ &9=4x\\ &x=\frac{9}{4} \end{aligned}

Area CAB

\begin{aligned} &=\int_{0}^{\frac{9}{4}}(3-2\sqrt{x})dx\\ &=\left [ 3x-\frac{2x^{\frac{3}{2}}}{\frac{3}{2}} \right ]_{0}^{\frac{9}{4}}\\ &=\left [ 3x-\frac{4}{3}x^{\frac{3}{2}} \right ]_{0}^{\frac{9}{4}}\\ &=3\left ( \frac{9}{4} \right )-\frac{4}{3}\left ( \frac{9}{4} \right )^{\frac{3}{2}}-0+0\\ &=\frac{27}{4}-\frac{4}{3}\left ( \left ( \frac{3}{2} \right )^{2} \right )^{\frac{3}{2}}\\ &=\frac{27}{4}-\frac{4}{3}\times \frac{27}{8}\\ &=\frac{27}{4}-\frac{9}{2}\\ &=\frac{9}{4} \end{aligned}

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Gurleen Kaur

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