Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

Remember that integration is the inverse procedure to differentiation. So, if you can do trigonometric differentiation, you can do trig integration.

In this paper, we first establish the quadrature formulae of proper integrals with weight by trigonometric interpolation. Then we use the method of separation of singularity to derive the quadrature ...