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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_0^\pi  {} $ $(x · sin^2x · cos x) dx $ =
  • A
    $0$
  • B
    $2/9$
  • C
    $- 2/9$
  • ✓
    $- 4/9$
✓

Answer

Correct option: D.
$- 4/9$
d
$\int\limits_0^\pi  {x\,\cdot\,({{\sin }^2}x\;\cos x)\,dx} $= $x\,\cdot\,\left. {\frac{{{{\sin }^3}x}}{3}} \right|_{\,0}^{\,\pi } - \int\limits_0^\pi  {\frac{1}{3}{{\sin }^3}x\;dx} $

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