Int vs Integral; Int giving wrong results

Suppose I have the function

    p=@(x) (heaviside(x-0.2)-heaviside(x-0.3)).*(x.^3+x.^2+x+1)+(heaviside(x-0.3)-heaviside(x-0.8)).*(-3*x.^3-2*x.^2+3*x+0.77)

which basically comes from using cubic splines to interpolate functions. I want to calculate the integral of p(r)^2/r between 1 and some number S, ideally symbolically.

If I do integral then I get:

    integral( @(s)(p(s)).^2./s,1,0.3)=-1.601

If instead I use int:

syms S
g=matlabFunction(int( @(s)(p(s)).^2./s,1,S),'Vars', {S}); 
g(0.3)=0

Clearly the int is giving the wrong result, but I don't know why. This example comes from a much more complicated example where integral gives the right result, and in the other case int gives non zero results but they are very wrong.

I would like to use int but I need to understand why it is giving such wrong results!

Thanks,

James

Answer 1

[Christopher Creutzig]

As the documentation says down in the “Tips” section, int(f,1,S) assumes that 1 ≤ S. In that region, your input function is 0, so int returning 0 is correct. Call int(f,S,1) to get a result valid for S ≤ 1.

Answer 2

[Walter Roberson]

int() does not take a function handle as an argument.

syms s
g = matlabFunction( int((p(s)).^2./s,1,S), 'vars', S);