_ ,0 ^ ,3 |2 - x|dx equals - Vidyadip

MCQ

$\int_{\,0}^{\,3} {|2 - x|dx} $ equals

A
$2/7$
✓
$5/2$
C
$3/2$
D
$ - 3/2$

✓

Answer

Correct option: B.

$5/2$

b
(b) $I = \int_0^3 {|2 - x|dx} $

$ = \int_0^2 {(2 - x)} \,dx + \int_2^3 { - (2 - x)\,dx} $

$ = \int_0^2 {(2 - x)} \,dx - \int_2^3 {\,(2 - x)\,dx} = \left[ {2x - \frac{{{x^2}}}{2}} \right]_0^2 - \left[ {2x - \frac{{{x^2}}}{2}} \right]_2^3$

$\Rightarrow$ $I = [4-2] - \left[ 6- \frac{{9}}{{2}} - (4-2) \right] $

$ = 2 - \left[ {4 - \frac{9}{2}} \right]$$ = \frac{5}{2}$.

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