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  • Need solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 11

Need solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 11

Answers (1)

Answer:

 (b)

Hint:

 Integration

Given:

 y^{2}=4ax, x^{2}=4ay

Explanation:

\begin{aligned} &\left ( \frac{x^{2}}{4a} \right )^{2}=4ax\\ &\frac{x^{4}}{16a^{2}}=4ax\\ &x^{4}-64a^{3}x=0\\ &x(x^{3}-64a^{3})=0\\ &x=0 \quad x=4a \end{aligned}

Area,

\begin{aligned} &=\int_{0}^{4a}\left [ 2\sqrt{ax}-\frac{x^{2}}{4a} \right ]dx\\ &=\left [ 2\sqrt{a}\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{3}}{12a} \right ]_{0}^{4a}\\ &=\frac{4}{3}\sqrt{a}(4a)^{\frac{3}{2}}-\frac{(4a)^{3}}{12a}-0\\ &=\frac{4}{3}\sqrt{a}2a^{\frac{3}{2}}-\frac{16a^{2}}{3}\\ &=\frac{32a^{2}}{3}-\frac{16a^{2}}{3}\\ &=\frac{16a^{2}}{3} \end{aligned}

Posted by

Gurleen Kaur

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