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Model Paper 3 — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsModel Paper 31 Mark
MCQ
$\int_{-\pi}^\pi \sin ^5 x d x=?$
  • A
    $\frac{5 \pi}{16}$
  • B
    $2 \pi$
  • ✓
    $0$
  • D
    $\frac{3 \pi}{4}$
✓

Answer

Correct option: C.
$0$
(c) 0
Explanation: If f is an odd function,
$\int_{-a}^a f(x) d x=0$
as, $\int_0^a f(x) d x=-\int_{-a}^0 f(x) d x$
$f(x)=\sin ^5 x$
$f(-x)=\sin ^5(-x)$
Therefore, $f(x)$ is odd number $\int_{-\pi}^\pi \sin ^5 x d x=0$

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