How to integrate using only symbolic variables, or variables in general?

syms A f0 t0 f0
ft = piecewise(0<=t<=t0/2,A.*sin(2.*pi.*f0.*t),t0/2<=t<=t0, 0);
a0 = 1/t0.*int(A.*sin(2.*pi.*f0.*t),t,0,t0./2)
simplify(a0)
pretty(a0)

I am trying to integrate the function A*sin(2*pi*f0*t) from 0 to t0/2, however whenever I run my script, the output is clearly the incorrect evaluation seen below:

       / pi f0 t0 \2
  A sin| -------- |
       \     2    /
  ------------------
       f0 t0 pi

This is for calculating the fourier coefficient a0, using basic integration for a half-wave rectified sine wave, and the expected result is A/pi.

Any suggestions that could point me in the right direction would be greatly appreciated!

Answer 1

[Chaitral Date]

 I executed the above code and observed the same output. The method which you are using is the appropriate way to find out definite integral of a symbolic expression. Hence the output which we are observing is correct.