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  • Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 36 Maths.

Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 36 Maths.

Answers (1)

Answer:

4 \pi sq. Units

Hints:

Use concept.

Given:

The first quadrant enclosed by x-axis, the line  y = x  and the circle x^2+y^2=32

Solution:

Point of intersection, x =4

Area of a shaded region = \int_{0}^{4} x d x+\int_{4}^{4 \sqrt{2}} \sqrt{32-x^{2}} d x

\begin{aligned} &=\left[\frac{x^{2}}{2}\right]_{0}^{4}+\left[\frac{x}{2} \sqrt{32-x^{2}}+16 \sin ^{-1} \frac{x}{4 \sqrt{2}}\right]_{4}^{4 \sqrt{2}} \\ &=8+16 \frac{\pi}{2}-8-4 \pi=4 \pi=4 \pi \text { Sq.units. } \end{aligned}

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