I'm not sure what you are actually trying to do. Radial velocity isn't generally measured, it is computed from the projected velocity. But if I take you at your word, that your raw data is radial velocity, then that simplifies things.
If you know the period, $P$, and you know the $v$ AND if you know the theoretical relationship between them $v = f(p)$ then you can use linear least squares to compute the adjustable parameters of $f(p)$ by plotting $v$ (measured) vs $v$(calculated).
Any 'best fit' equation is able to interpolate values of $v$ so all you need to divide up the period into small intervals and approximate the area under the curve using its two end-points (it is rarely necessary to use parabolic fits that also use the mid-points of those small intervals).
Thus the problem of integration becomes one of simple geometry (you have a tall thin rectangle with a triangle on top of it for each interval). Let's think about a star with a 30 day period. That's ~40,000 minutes, so I'd probably use 5 or 8 minute intervals ...starting at minute 0 what's the area under the curve from t=0 to t=8 minutes? then from 8 to 16, all the way up to 43,200th minute. Sum of those areas is total area. An Excel spreadsheet can easily do that.
Actually, if you also use 5 minute intervals and compare the results you'll see how much better (hopefully NOT much) a smaller interval is...analytical integration is this taken to the limit of the interval approaching zero, but in real life, numerical integration is necessary for almost all 'interesting' problems. Here are 2 links, fwiw: