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Question
The value of `int_(-pi)^pi sin^3x cos^2x "d"x` is ______.
Solution
The value of `int_(-pi)^pi sin^3x cos^2x "d"x` is 0.
Explanation:
Let I = `int_(-pi)^pi sin^3x cos^2x "d"x`
Let f(x) = sin3x cos2x
f(–x) = sin3(– x) cos2(– x)
= – sin3x cos2x
= – f(x)
∴ `int_(-pi)^pi sin^3 x cos^2 x "d"x` is an odd function
∴ I = 0
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