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The Trapezoidal Rule for Increasing Functions

​
n
4
Let
a=
x
0
<
x
1
<…<
x
n-1
<
x
n
=b
be a partition of
[a,b]
, with
x
i+1
-
x
i
=
b-a
n
; then:
b
∫
a
f(x)dx
≈ the sum of the rectangle areas + the sum of the triangle areas =
n-1
∑
i=0
f(
x
i
)
b-a
n
+
1
2
(f(
x
n
)-f(
x
0
))
b-a
n
.
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