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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
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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