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  • Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 18.

Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 18.

Answers (1)

Answer:

9 sq. units.

Hint:use basic concepts.

Given:

he given equations of the curves are

y=\sqrt{x}, x=2y+3

Solution:   We have,

y=\sqrt{x}, x=2y+3

Solving we get,

\begin{aligned} &y=\sqrt{2 y+3}, y \geq 0 \\ &y^{2}=2 y+3, y \geq 0 \\ &y^{2}-2 y-3=0, y \geq 0 \\ &(y-3)(y+1)=0, y \geq 0 \\ &y=3 \end{aligned}

 

The graph of function y=\sqrt{x}  is part of parabolay=x^2  lying above x  –axis.

The graph is as shown in the figure.

From the figure, area of shaded region,

\begin{aligned} A &=\int_{0}^{3}\left(2 y+3-y^{2}\right) d y \\ &=\left[\frac{2 y^{2}}{2}+3 y-\frac{y^{3}}{3}\right]_{0}^{3} \\ &=\left[\frac{18}{9}+9-9-0\right] \\ &=9 \text { sq units } \end{aligned}

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