In[]:=
f[t_]=Piecewise[{{0,t<=-1},{2*Sqrt[1-t^2]/Pi,-1<t<1},{0,t>=1}}]
Out[]=
0
t≤-1
2
1-
2
t
π
-1<t<1
0
True
In[]:=
c[t_]=2*Integrate[f[tau]*f[t-tau],{tau,-Infinity,Infinity}]
Out[]=
2
0
t≥2||t≤-2
Integrate
0
t-tau≤-1
2
1-
2
(t-tau)
π
-1<t-tau<1
0
True
0
tau≤-1
2
1-
2
tau
π
-1<tau<1
0
True
,{tau,-∞,∞},Assumptions-2<t<2
True
In[]:=
Plot[c[t],{t,0,2}]
Out[]=
In[]:=
​