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

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

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

= \frac{1}{2}

 

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