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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Evaluate $\int\limits_{ - 1}^1 {{{\sin }^5} \ x{{\cos }^4} \ xdx} $
✓

Answer

Let f(x) = sin5x.cos4x
f(-x) = sin5(-x).cos4(-x)
= -sin5x.cos4x
= -f(x)
$\therefore$  f is odd function
$\therefore \int\limits_{ - 1}^1 {{{\sin }^5}x.{{\cos }^4}xdx = 0} $

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