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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int_{}^{} {{{\sin }^3}x\;.\;\cos x\;dx = } $
  • A
    $\frac{{{{\sin }^4}x{{\cos }^2}x}}{8} + c$
  • ✓
    $\frac{{{{\sin }^4}x}}{4} + c$
  • C
    $\frac{{{{\sin }^2}x}}{2} + c$
  • D
    $4{\sin ^4}x + c$
✓

Answer

Correct option: B.
$\frac{{{{\sin }^4}x}}{4} + c$
b
(b)$\int_{}^{} {{{\sin }^3}x\,.\,\cos x\,dx} $. Put $\sin x = t,$ then
$\cos x\,dx = dt$; $\int_{}^{} {{t^3}dt} = \frac{{{t^4}}}{4} = \frac{{{{\sin }^4}x}}{4} + c$.

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