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

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Grant Griffin on 16 Apr 2017
Answered: Chaitral Date on 24 Apr 2017
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!
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### Answers (1)

Chaitral Date on 24 Apr 2017
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.
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