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  • Need solution for RD sharma maths class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 9

Need solution for RD sharma maths class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 9

Answers (1)

\frac{8a^{2}}{3} sq.units

Hint:

Use this formula to integrate : \int_{a}^{b}x^{n}dx=\left [ \frac{x^{n+1}}{n+1} \right ]_{a}^{b}
Given:y^{2}=4ac, latus-rectum

Explanation:

Latus-rectum(x=a)

Area \begin{aligned} =2 \int_{0}^{a} 2 \sqrt{a x} d x \\ \end{aligned}

\begin{aligned}&=2 \times 2\left[\sqrt{a} \frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_{0}^{a} \\ \end{aligned}

\begin{aligned}&=2 \times \frac{4}{3} \sqrt{a}\left[a^{\frac{3}{2}}-0\right] \quad\left[\because \int_{a}^{b} x^{n} d x=\left[\frac{x^{n+1}}{n+1}\right]_{a}^{b}\right] \\ \end{aligned}

=\frac{8a^{2}}{3} sq.units

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