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  • Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 51.

Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 51.

Answers (1)

Answer:

M=2.

Hints:

Use concept of definite integrals

Given:

The parabola y^2=4ax and the line y = mx is \frac{a^2}{12} .

Solution:

Area of the bounded region = \frac{a^2}{12}

\begin{aligned} &\frac{a^{2}}{12}=\int_{0}^{a} \sqrt{4 a x}-m x d x \\ &\frac{a^{2}}{12}=\left[2 \sqrt{a} \frac{x^{\frac{1}{2}}}{\frac{3}{2}}-m \frac{x^{2}}{2}\right]_{0}^{a} \end{aligned}

\begin{aligned} &\frac{a^{2}}{12}=\frac{4 a^{2}}{3}-m \frac{a^{2}}{2} \\ &m=2 \end{aligned}

Therefore, the value of m is 2.

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