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  • Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 16 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 16 Maths Textbook Solution.

Answers (1)

Answer:  5

Hint: You must know the rules of solving definite integral.

Given:

                \int_{0}^{4}|x-1| d x

Solution:

                \begin{aligned} &\mathrm{I}=\int_{0}^{4}|x-1| d x \\ & \end{aligned}

                |x-1|=\left\{\begin{array}{l} -(x-1), 0 \leq x \leq 1 \\ x-1, \quad 1 \leq x \leq 4 \end{array}\right\}

                \begin{aligned} I &=\int_{0}^{1}-(x-1) d x+\int_{1}^{4}(x-1) d x \\ & \end{aligned}

                =\left[-\left(\frac{x^{2}}{2}-x\right)\right]_{0}^{1}+\left[\frac{x^{2}}{2}-x\right]_{1}^{4} \\

                =\frac{1}{2}+8-4+\frac{1}{2}=4+1 \\

                I =5

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