Evaluate `int_-1^ 1 sin^5xcos^4xdx`

1.	Evaluate `int_-1^ 1 sin^5xcos^4xdx`
Answer» Here,` f(x) = int_-1^1sin^5xcos^4xdx` If we find, `f(-x)`, `f(-x) = int_-1^1sin^5(-x)cos^4(-x)dx` `=int_-1^1-sin^5xcos^4xdx=-int_-1^1sin^5xcos^4xdx` `=-f(x)` that means f(x) is an odd function. We know, `int_-a^af(x)dx = 0`, if f(x) is an odd function. Thus,`int_-1^1sin^5xcos^4xdx = 0`

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