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  • Need solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 27

Need solution for RD Sharma maths class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 27

Answers (1)

Answer:

 (c)

Hint:

 Integration

Given:

 y=x\left | x \right |,\: x=-1,\: x=1

Explanation:

y=x\left | x \right |=\left\{\begin{matrix} x^{2} &x> 0 \\ -x^{2} & x< 0 \end{matrix}\right.

Area of bounded region,

=\int_{-1}^{1}x\left | x \right |dx

Area AOB,

\begin{aligned} &=\int_{-1}^{0}-x^{2}dx\\ &=\left [ \frac{-x^{3}}{3} \right ]_{-1}^{0}\\ &=\frac{-1}{3} \end{aligned}

Area is always positive,

\begin{aligned} &=-\left ( \frac{-1}{3} \right )=\frac{1}{3} \end{aligned}

Area OCD,

\begin{aligned} &=\int_{0}^{1}x^{2}dx\\ &=\left [ \frac{x^{3}}{3} \right ]_{0}^{1}\\ &=\frac{1}{3} \end{aligned}

Total area

\begin{aligned} &=\frac{1}{3}+\frac{1}{3}\\ &=\frac{2}{3} \end{aligned}

Posted by

Gurleen Kaur

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