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

MCQ

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

✓
$5/2$
B
$1/2$
C
$3/2$
D
$7/2$

✓

Answer

Correct option: A.

$5/2$

a
(a) $I = \int_{ - 1}^2 {\,|x|dx} $$ = \int_{ - 1}^0 { - x\,dx} + \int_0^2 {x\,\,dx} $

$ = - \left[ {\frac{{{x^2}}}{2}} \right]_{ - 1}^0 + \left[ {\frac{{{x^2}}}{2}} \right]_0^2$

$ = - \left[ {0 - \frac{1}{2}} \right] + [2]$

$ = 2 + \frac{1}{2} = \frac{5}{2}$.

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