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Integration Using Substitution

∫ -1 1 | 1-x ...

Question

$\int_{- 1}^{1} | 1 - x | d x$ is equal to:

- 2

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0

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2

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4

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Solution

The correct option is C $2$
We know, for $x \leq 1$ , we have $1 - x \geq 0$ thus $| 1 - x | = 1 - x$
Let $I = \int_{- 1}^{1} | 1 - x | d x$
$= \int_{- 1}^{1} (1 - x) d x$
$= {(x - \frac{x^{2}}{2})}_{- 1}^{1}$
$= 1 - \frac{1}{2} - (- 1 - \frac{1}{2}) = 1 + 1 = 2$

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