I have created the following symbolic integral:
syms x;
syms t;
int(1./((1-t.*x).^3),t,0,1)
ans =
piecewise([x = 1, Inf], [not 1/x in (0, 1) and x 1, -(x/2 - 1)/(x - 1)^2])
which results in a piecewise function definition. Now I want to plot this integral using the ezplot function, but this leads to an error:
Error using ezplot (line 162)
piecewise([1/x in Dom::Interval([0], [1]), -int(1/(t*x - 1)^3, t, 0, 1)],
[~1/x in Dom::Interval([0], [1]), -(x - 2)/(2*(x - 1)^2)])
cannot be plotted in the xy-plane.
Error in sym/ezplot (line 61)
h = ezplot(fhandle(f));
How can I plot this piecewise symbolic integral?
Though I could not find any evidence by Mathworks, it seems that ezplot does not work together with piecewise symbolic functions (Source: there are a few open questions on exactly this topic in the Matlab help forum).
In this answer I am presenting a work-around, which works for explicit, invertible functions, i.e. it will fail for stuff like x^2 + y^2 = 1 or y^2 = y^4 , and similar stuff. In this special case (which I assume is used most often), one can manually generate a x-vector and calculate the corresponding y-values using the subs function.
The default range for ezplot is [-2pi, 2pi]. The number of points depends strongly on the function, but with around 1000 points, a reasonably smooth plot should be created. Note: This should produce the default ezplot behavior. If you have further knowledge about the function, i.e. value ranges etc., you should definitely use this to create the x vector.
xp = -2*pi : 0.01: 2*pi;
yp = subs(f, x, xp);
plot(xp,yp);