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STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
The value of $12 \int \limits_0^3\left|x^2-3 x+2\right| d x$ is $.............$
  • A
    $20$
  • B
    $25$
  • ✓
    $22$
  • D
    $65$
✓

Answer

Correct option: C.
$22$
c
$12 \int \limits_0^3\left| x ^2-3 x +2\right| dx$

$={ }_{12} \int_0^3\left|\left( x -\frac{3}{2}\right)^2-\frac{1}{4}\right| dx$

If $x-\frac{3}{2}=t$

$dx = dt$

$=24 \int \limits_0^{3 / 2}\left| t ^2-\frac{1}{4}\right| dt$

$=24\left[-\int^{1 / 2}\left(t^2-\frac{1}{4}\right) d t+\int \limits_0^{3 / 2}\left(t^2-\frac{1}{4}\right) d t\right]=22$

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