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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 20 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 20 maths

Answers (1)

Answer: 2

Hint: You must know about \left | x \right | function.

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

Solution:  

Let I=\int_{-1}^{1}|1-x| d x

We know |1-x|=\left\{\begin{array}{c} 1-x \quad ; \quad 1-x \geq 0 \\ -x \geq-1 \Rightarrow x \leq 1 \\\\ -(1-x) ; \quad 1-x<0 \\ -x<-1 \Rightarrow x>1 \end{array}\right\}

\therefore \int_{-1}^{1}|1-x| d x=\int_{-1}^{1}(1-x) d x

                               \begin{aligned} &=\int_{-1}^{1} 1 d x-\int_{-1}^{1} x \; d x \\\\ &=\left[x-\frac{x^{2}}{2}\right]_{-1}^{1} \end{aligned}

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

 

 

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