Find ʃ sin3 x (cos x)dx, if the limits of integration are π (upper) and 0 (lower).

Answer 1

∫_{(from 0 to π)} [sin³x cosx] dx

Let u = sinx. Then du = cosxdx.

When x = 0, u = sin0 = 0

When x = π, u = sinπ = 0

So, the given integral is equivalent to ∫_{(from 0 to 0)} u³du = 0