Question

Evaluate the integral from -4 to 4 of [x^3 sin(6x)] / [sin(5x)]dx
This is one of those freebies. Note that the function is odd: f(-x) = -f(x), and the curve is symmetric around (0,0).

That means that the value from -4 to 0 is negative the value from 0 t0 4, so the whole integral is zero.

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