Rick, there is: if F'(x) = f(x), then integral f(x) dx = F(x) + C C is any constant
so the integral result has some shift along y axis. The shift should be determined by boundary conditions.
"Timothy E. Vaughan" <tvaughan@_NO_SPAM_bwh.harvard.edu> wrote in message <email@example.com>... > > ""Leung, Randolph [COPE/HKG]"" <RckLeung@Copeland-Corp.com> wrote in message > news:9B636583813BD311BE6400508B10481F6C5274@fs83.hk.copeland-sid.com... > > > > I have some experimental time traces to integrate. CUMTRAPZ seems > > to be a simple and easy option for me. To test it, I tried to integrate a > > simple SIN(X) time trace as follows, > > > > x = 0:pi/100:4*pi]; > > y = sin( 2*pi*x). > > > > inty = cumtrapz( x', y' ); > > > > I would expect a COS(X) time trace after CUMTRAPZ. The integrated > > time trace gave a cos pattern of variation, correct amplitude BUT was > > wrong in phase and shifted upwards, i.e. it is greater than zero for all > > x and gives 0, rather than 1, at x = 0. I am very confused with the > > results. > > It seems you may be forgetting a bit of your calculus. You are numerically > taking the INDEFINITE integral of your function. In that case, you must be > prepared to add a constant to your solution. [I think it is really only > shifted "upward", and not really wrong in phase.] You need to determine the > appropriate constant from other conditions of your problem. > > Tim > > >