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Model Paper 3 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 31 Mark
Question
$\int_{-\pi}^\pi \sin ^5 x d x=?$
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Answer

(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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