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  • Provide Solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 8

Provide Solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 8

Answers (1)

Answer:  40

Hint: Break the range of integration and then solve.

Given:   \begin{aligned} &\int_{-6}^{6}|x+2| d x \\ & \end{aligned}

             x+2=0, x=-2

Solution:

                \begin{aligned} \int_{-6}^{6}|x+2| d x & \\ \end{aligned}

                 \left\{\begin{array}{ll} -(x+2), & -6 \leq x \leq-2 \\ (x+2), & -2 \leq x \leq-6 \end{array}\right\}

                \begin{aligned} &=\int_{-6}^{-2}-(x+2) d x+\int_{-2}^{6}(x+2) d x \\ & \end{aligned}

               =\left[-\left(\frac{x^{2}}{2}+2 x\right)\right]_{-6}^{-2}+\left(\frac{x^{2}}{2}+2 x\right)_{-2}^{6} \\

               =-2+4+18-12+18+12-2+4=40

               

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