Trapezoidal Rule for Integration
Split sum
I
=
∑
i
=
1
n
h
f
x
i
2
+
∑
i
=
1
n
h
f
x
1
+
i
2
Adjust limits
I
=
∑
i
=
0
-1
+
n
h
f
x
i
2
+
∑
i
=
1
n
h
f
x
i
2
Peel terms
I
=
2
∑
i
=
1
-1
+
n
h
f
x
i
2
+
h
f
x
0
2
+
h
f
x
n
2