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  • Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 38 Maths.

Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 38 Maths.

Answers (1)

Answer:

\frac{9}{2} sq. Units

Hints:

Use concept .

Given:

x^2=y is a parabola line y=x+2

Solution: x^2=y  is a upward parabola line y=x+2

They meet at pts (2,4) and (-1,1)

By solving the equation,

\begin{aligned} &x^{2}=y, y=x+2 \\ &\Rightarrow x^{2}-x-2=0 \\ &\Rightarrow x=2 \text { or }-1 \\ &\Rightarrow x=4 \text { or } 1 \end{aligned}

 Required area

= \int_{-1}^{2} Area of line - \int_{-1}^{2} Area of parabola

 

\begin{aligned} &=\int_{-1}^{2}(x+2) d x-\int_{-1}^{2} x^{2} d x \\ &=\left[\frac{x^{2}}{2}\right]_{-1}^{2}+[2 x]_{-1}^{2}-\left[\frac{x^{3}}{3}\right]_{-1}^{2} \\ &=\frac{4}{2}-\frac{(-1)^{2}}{2}+2 * 2-(2 *-1)-\left(\frac{2^{3}}{3}-\frac{(-1)^{3}}{3}\right) \\ &=2-\frac{1}{2}+4+2-\left(\frac{8}{3}+\frac{1}{3}\right) \\ &=8-\frac{1}{2}-3=5-\frac{1}{2}=\frac{9}{2} \text { sq.units } \end{aligned}

 

 

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