_ - 1 ^1 x^ 17 ^4 x ,dx = - Vidyadip

Question

$\int_{ - 1}^1 {{x^{17}}{{\cos }^4}x} \,dx = $

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Answer

c
(c) Let $f(x) = {x^{17}}{\cos ^4}x$

$f( - x) = {( - x)^{17}}{\left\{ {\cos ( - x)} \right\}^4} = - f(x)$

Therefore, $\int_{ - 1}^1 {{x^{17}}{{\cos }^4}x\,dx = 0} $.

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