In[]:=
p[x_,a_,b_]:=2(x-a)/(a-b)^2Boole[a<x<b];​​Integrate[p[x,a,b],{x,a,b}]/.{a-1,b1}
Out[]=
1
In[]:=
Plot[p[x,a,b],{x,a,b}]/.{a-1,b1}
Plot
:Limiting value a in {x,a,b} is not a machine-sized real number.
Out[]=
​
In[]:=
conv=Integrate[p[x,a,b]p[y-x,a,b],{x,-Infinity,Infinity}]//Simplify
Out[]=
-
2
3
(2a-y)
3
4
(a-b)
a<b&&2a<y&&a+b≥y
2(2b-y)(6
2
a
-2
2
b
-6ay+2by+
2
y
)
3
4
(a-b)
a<b&&a+b<y&&2b>y
0
True
In[]:=
Integrate[conv,{y,2a,2b}]/.{a-1,b1}
Integrate
:Unable to prove that integration limits {2a,2b} are real. Adding assumptions may help.
Out[]=
1
In[]:=
Plot[conv/.{a-1,b1},{y,-2,2}]
Out[]=