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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate $\int\limits_{ - 1}^1 {{{\sin }^5} \ x{{\cos }^4} \ xdx} $
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Answer

Let $f(x) = \sin^5x.\cos^4x$
$f(-x) = \sin^5(-x).\cos^4(-x)$
$= -\sin^5x.\cos^4x$
$= -f(x)$
$\therefore f$ is odd function
$\therefore \int\limits_{ - 1}^1 {{{\sin }^5}x.{{\cos }^4}xdx = 0} $

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