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Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 30 Maths Textbook Solution.

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Answer:  2

Given:   \int_{1}^{2}\left|x^{2}-2 x\right| d x

Hint: Open the mode and then do integration by parts


\int_{1}^{2}\left|x^{2}-2 x\right| d x

\begin{aligned} &=\int_{1}^{2}-\left(x^{2}-2 x\right) d x+\int_{2}^{3}\left(x^{2}-2 x\right) d x \\ & \end{aligned}


\begin{aligned} &=\frac{-8}{3}+4+\frac{1}{3}-1+9-9-\frac{8}{3}+4 \\ & \end{aligned}

=7-\frac{15}{3} \\

=\frac{21-15}{3} \\


= 2

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