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  • Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 4 maths

Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 4 maths

Answers (1)

Answer:

 (b)

Hint:

 Find the region between parabola and line

Given:

 y=2-x^{2},\quad x+y=0

Explanation:

To find the point of intersection of

y=2-x^{2} \text { and } x+y=0

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

Area of the region ABCD,

\begin{aligned} &A=\int_{-1}^{2}(2-x^{2}-(-x))dx \\ &=\int_{-1}^{2}(2-x^{2}+x)dx \\ &=\left [ 2x-\frac{x^{3}}{3}+\frac{x^{2}}{2} \right ]_{1}^{2} \\ &=\left [ 2(2)-\frac{(2)^{3}}{3} +\frac{(2)^{2}}{2}\right ]-\left [ 2(-1)-\frac{(-1)^{3}}{3} +\frac{(-1)^{2}}{2} \right ] \\ &=\left [ 4-\frac{8}{3}+2 \right ]-\left [ -2+\frac{1}{3}+\frac{1}{2} \right ] \\ &=6-\frac{8}{3}+2-\frac{1}{3}-\frac{1}{2} \\ &=5-\frac{1}{2} \\ &=\frac{9}{2}sq.units \end{aligned}

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Gurleen Kaur

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