_ -1 ^1 |x-2| x-2 d x, x 2 is equal to - Vidyadip

MCQ

$\int_{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2$ is equal to

A
1
B
-1
C
2
D
-2

✓

Answer

Let $I=\int_{-1}^1 \frac{|x-2|}{x-2} d x$
$
=\int_{-1}^1 \frac{-(x-2)}{x-2} d x=\int_{-1}^1-1 \cdot d x=[-x]_{-1}^1=-[1-(-1)]=-2
$

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