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  • Need solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 22.

Need solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 22.

Answers (1)

Answer:

\frac{32}{3} sq. Units

Hint:

Use concept.

Given:

The given  equations are y=2x^2  and y=x^2+4  

Solution:

To find the area enclosed by,

y=2x^2        ........(i)

y=x^2+4        ........(ii)

On solving the equation (i) and (ii),

2x^2=x^2+4

or x^2=4

or x=\pm 2

\therefore y=8

 Equation (1) represents a parabola with vertex (0, 0) and axis as y - axis.

 Equation (2) represents a parabola with vertex (0,4) and axis as the y - axis.

 Points of intersection of parabolas are A(2, 8) and B(– 2, 8).

These are shown in the graph below:

Required area=Region AOBCA

                          =2(RegionAOCA)

\begin{aligned} &=2 \int_{0}^{2}\left(x^{2}+4-2 x^{2}\right) d x \\ &=2 \int_{0}^{2}\left(4-x^{2}\right) d x \\ &=2\left[4 x-\frac{x^{3}}{3}\right]_{0}^{2} \\ &=2\left[\left(8-\frac{8}{3}\right)-0\right] \\ &=\frac{32}{3} \text { sq.units } \end{aligned}

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