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Evaluate int_-1^1 sin^5x cos^4x dx

Answer»

Solution :Let I = `int_-1^1 sin^5x cos^4x dx`
Let f(x) = `sin^5x cox^4x`. Then
`f(-x) = sin^5(-x) cos^4(-x)`
=`-sin^5x cos^4x = -f(x)`
i.e., f is an ODD FUNCTION.
THEREFORE, by PROPERTY 8(II), I = 0.


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