Eqn 1
Use complex notation for the sin
Eqn 2
Note that with
Eqn 3
So that
Eqn 4
In the usual way let
Eqn 5
The trap rule estimate of the integrals is then
Eqn 6
Note that there are no – signs on the alternate steps. This is because the sum naturally starts from zero rather than from negative infinity.