Did you define your symbolic variables first?
syms a x y p
You'll need to give a numeric value for p or else int won't be able to evaluate it:
p=2;
You can redefine your function in terms of a heaviside function. Now you can integrate it:
fint = int(heaviside(y-a)*(y-a)^p,a,x)
fint =
-(a - x)^3/3
If you want to get an answer for a given a and x, you can substitute:
subs(fint,{a,x},{sym(-1),sym(1)})
ans =
8/3
double(ans)
ans =
2.6667
EDIT: As Susan points out, this gives the wrong answer for a<x. This seems to occur because one of the integral limits, a, is also a parameter in the equation. This code gives the correct answer:
syms a x x0 x1 y p
p=2;
fint = int(heaviside(y-a)*(y-a)^p,y,x0,x1);
subs(fint,{x0,x1},{a,x})
ans =
-(heaviside(x - a)*(a - x)^3)/3
subs(fint,{x,a},{sym(2),sym(1)})
ans =
1/3
subs(fint,{x,a},{sym(1),sym(2)})
ans =
0
