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

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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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