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  • Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Region exercise 20.3 question 31 Maths.

Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 31 Maths.
 

Answers (1)

Answer:

\frac{11}{6}\text{sq. units}

Hint:

Use concept.

Given:

The given equation are y =x and y =x^2+2 .

Solution:  To find area bounded by x =0, x =1

and

y =x        ........(1)

y =x^2+2........(2)

Equation(1)  is a line passing through (2,2) and (0,0).Equation (2) is a parabola upward with vertex at (0,2).

A rough sketch of curve is as under:

Shaded region is sliced into rectangle of area=. .It slides from to ,so

Required Area=Region OABCO

\begin{aligned} A &=\int_{0}^{1}\left(y_{1}-y_{2}\right) d x \\ &=\int_{0}^{1}\left(x^{2}+2-x\right) d x \\ &=\left[\frac{x^{3}}{3}+2 x-\frac{x^{2}}{2}\right]_{0}^{1} \\ &=\left[\left(\frac{1}{3}+2-\frac{1}{2}\right)-0\right] \\ &=\left(\frac{2+12-3}{6}\right) \\ &=\frac{11}{6} \text { sq.units } \end{aligned}

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