In[]:=
f[t_]=2
-
3
160
(-32+40
2
t
-20
3
t
+
5
t
)
0≤t<2
0
True
Out[]=
2
-
3
160
(-32+40
2
t
-20
3
t
+
5
t
)
0≤t<2
0
True
In[]:=
Plot[f[t],{t,0,2}]
Out[]=
In[]:=
g[t_]=Integrate[f[tau]*f[t-tau],{tau,-Infinity,Infinity}]
Out[]=
-
7
(-4+t)
(80+536t+228
2
t
+28
3
t
+
4
t
)
1971200
2≤t<4
2838528t-2365440
3
t
+887040
4
t
+147840
5
t
-103488
6
t
+7920
7
t
+1320
8
t
-220
9
t
+
11
t
1971200
0<t<2
0
True
In[]:=
Integrate[g[t],{t,0,4}]
Out[]=
1
In[]:=
a1=Integrate[g[t],{t,0,4/Sqrt[3]}]
Out[]=
88347959-48611328
3
4209975
In[]:=
a2=Integrate[g[t],{t,4/Sqrt[3],4}]
Out[]=
2048(-41083+23736
3
)
4209975
In[]:=
a=Simplify[a1+a2]
Out[]=
1
In[]:=
a2=NIntegrate[g[t],{t,4/Sqrt[3],4}]
Out[]=
0.014087