# Define curve by integral

tmelorc shared this question 2 years ago

Let p(x) be a function for x in [0,1], for example p(x)=cos(x).

How to plot the curve given by a(t)=\int_0^t p(s)ds for t in [0,1], for example?

I suspect that Geogebra can not work with functions if the variable is not x.

1

The specific example given can be done by using the CAS to find the indefinite integral of p(x), but in general, I don't see a simple way to do this.

The best workaround I can come up with is to create a list of points on the curve using the sequence function. If you need a continuous approximation of the curve, you can fit a polynomial to these points, and restrict the domain to a closed interval (which effectively gives a Taylor Polynomial approximation of the curve).