Question

Evaluate the integral from -4 to 4 of [x^3 sin(6x)] / [sin(5x)]dx

Answer 1

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.