_ ,0 ^ ,2 ,|x - 1| ,dx = - Vidyadip

MCQ

$\int_{\,0}^{\,2} {\,|x - 1|\,dx = } $

A
$0$
B
$2$
C
$1/2$
✓
$1$

✓

Answer

Correct option: D.

$1$

d
(d) $I = \int_0^2 {|x - 1|dx }$

$={ \int_0^1 {( - x + 1)dx + \int_1^2 {(x - 1)\,dx} } } $

$ = \left( {\frac{{ - {x^2}}}{2} + x} \right)_0^1 + \left( {\frac{{{x^2}}}{2} - x} \right)_1^2 = 1.$

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