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  • Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 5 maths textbook solution

Answers (1)

Answer:

8\sqrt{3}\; sq\cdot units

Hint:

A=2 \times \text { Area of } O A B O

Given:

Draw rough sketch to indicate the region bounded between curve y^{2}=4 x and line x=3 .Also find the area of region.

Solution:

y^{2}=4 x  Represent parabola with vertex at x=3 line parallel toy-axis.

Since y^{2}=4 x is symmetrical axis

Area of corresponding rectangle =\left ( y \right )dx

\begin{aligned} &A=2 \times \text { Area of } O A B O \\\\ &A=2 \int_{0}^{3}|y| d x \\\\ &A=2 \int_{0}^{3} y d x \end{aligned}

\begin{aligned} &A=2 \int_{0}^{3} \sqrt{4 x} d x \\\\ &A=2 \times 2 \int_{0}^{3} \sqrt{x} d x \\\\ &A=4 \int_{0}^{3} \sqrt{x} d x \end{aligned}

\begin{aligned} &A=4\left[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_{0}^{3} \\\\ &=\frac{8}{3}\left[(x)^{\frac{3}{2}}\right]_{0}^{3} \\\\ &=\frac{8}{3} \times 3 \sqrt{3} \\\\ &=8 \sqrt{3} s q \cdot \text { unit } \end{aligned}                    \left[\because \int_{a}^{b} x^{n} d x=\left[\frac{x^{n+1}}{n+1}\right]_{a}^{b}\right]

       

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