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

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

Answers (1)

best_answer

Answer:  2

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

Hint: Open the mode and then do integration by parts

Solution:

\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}

=\left(\frac{-x^{3}}{3}+x^{2}\right)_{1}^{2}+\left(\frac{x^{3}}{3}-x^{2}\right)_{2}^{3}

\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} \\

=\frac{6}{3}

= 2

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