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  • Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 19

Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 19

Answers (1)

Answer: 0

Hint: you must know the rule of integration for function of x


Given: \int_{-1}^{1} x|x| d x

Solution:  I=\int_{-1}^{1} x|x| d x

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

\begin{aligned} &=-\frac{1}{3}\left[x^{3}\right]_{-1}^{0}+\frac{1}{3}\left[x^{3}\right]_{0}^{1} \\\\ &=-\frac{1}{3}[0-(-1)]+\frac{1}{3}[1-0] \end{aligned}

\begin{aligned} &=-\frac{1}{3}+\frac{1}{3} \\\\ &=0 \end{aligned}

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