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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$f (x) =$ $\int\limits_0^x {\,t\,(t\, - \,1)\,\,(t\, - \,2)\,dt} $ takes on its minimum value when:
  • A
    $x = 0 , 1$
  • B
    $x = 1 , 2$
  • ✓
    $x = 0 , 2$
  • D
    $x =$$\frac{{3\,\, + \,\,\sqrt 3 }}{3}$
✓

Answer

Correct option: C.
$x = 0 , 2$
c
$f ‘ (x) = x (x - 1) (x - 2) = 0$
$x = 0, 1, $ $or$ $ 2$
at $ x = 0 \& 2,$ $ f' (x)$  changes sign from $ - ve\ to\ + ve $ $\Rightarrow $ minimum

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