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Question
Prove the following:
`int_(-1)^1 x^17 cos^4 xdx = 0`
Solution
Let `I = int_(-1)^1 x^17 cos^4 x " dx" = 0`
Let f(x) = x17 cos4 x
f(-x) = (-x)17 cos4 (-x)
= - x17 cos4 x ....` [because int_(- a)^a f(x) = 0 "if" f(- x) = - f]`
∴ I = 0
∴ f (x) is an odd function, hence I = 0.
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