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Question
Evaluate: `int_(- pi/4)^(pi/4) x^3 sin^4x "d"x`
Solution
Let f(x) = x3.sin4x
∴ f(−x) = (− x)3 [sin (− x)]4
∴ − x3 (− sin x)4
∴ − f(x)
∴ f(x) is an odd function.
∴ `int_(- pi/4)^(pi/4) x^3 * sin^4x "d"x` = 0 ......`[∵ int_(-"a")^"a" "f"(x)"d"x` = 0, if f(x) is a odd function.]
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