Numerical Integration Examples

function

oscillator: f(x) =

c

1

+

c

2

sin(

c

3

2π x)

integration rule

Simpson's:

nd

2

order

c

1

0

c

2

1

c

3

-2.2

segments

3

limits

lower, a

0

upper, b

1

Numerical integration is a method used to calculate an approximate value of a definite integral

I=

b

∫

a

f(x)dx

. This Demonstration compares various Newton–Cotes methods to approximate the integrals of several different functions over the interval

[a,b]

. Typically, the error decreases as the order of the method is increased. Likewise, more segments usually leads to a more accurate approximation of the integral.