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Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 29 Maths Textbook Solution.

Answers (1)

Answer:  \frac{1}{2}

Given:  \int_{0}^{1}|2 x-1| d x

Hint: You must know how to open mode

Solution:  \int_{0}^{1}|2 x-1| d x

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

=\left(\frac{-2 x^{2}}{2}+x\right)_{0}^{\frac{1}{2}}+\left(\frac{2 x^{2}}{2}-x\right)^{\frac{1}{2}}

\begin{aligned} &=-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2} \\ & \end{aligned}

=-\frac{1}{4}+\frac{1}{2}-\frac{1}{4}+\frac{1}{2} \\


= \frac{1}{2}


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