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  • Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 16 maths

Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 16 maths

Answers (1)

Answer:

 (d)

Hint:

 Integration

Given:

 y=x^{2}+1,\: \: x+y=3

Explanation:

Intersection points are

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

Area

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

Posted by

Gurleen Kaur

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