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Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 25 maths textbook solution

Answers (1)

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Answer:

2

Given:

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

Hint:

To solve this equation we use \int \frac{x^{n}}{n+1}  formula.
 

Explanation:  
Let

\begin{aligned} &\int_{-1}^{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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