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Question
Evaluate the following using properties of definite integral:
`int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x`
Sum
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Solution
Let f(x) = `x^3 cos^3x`
f(– x) = `(- x)^3 cos^3 (- x)`
= `- x^3 cos^3 x`
= `- "f"(x)`
Here f(– x) = – f(x)
∴ f(x) is an odd function
∴ `int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x` = 0
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