Comparing Basic Numerical Integration Methods

function

-2x



magnifying tool

subintervals

4

method

left sum

right sum

midpoint

trapezoid

Simpson

2

∫

0

-2x



dx

approximate area = 0.28566 exact area = 0.49084

|error| = 2.05×

-1

10

Numerical integration methods are used to approximate the area under the graph of a function

f

over an interval

[a,b]

. Select a function and a method to visualize how the area is being approximated. Then increase the number of equal-width subintervals to see that more subintervals lead to a better approximation of the area. The effectiveness of various methods can be compared by looking at the numerical approximations and their associated errors. In particular, you can investigate how doubling the number of subintervals impacts the error. To use the magnifying tool, click anywhere in the graph for a closer look.

External Links

Numerical integration (Wolfram MathWorld)

Riemann Sum (Wolfram MathWorld)

Trapezoid Rule (Wolfram MathWorld)

Simpson's Rule (Wolfram MathWorld)

Numerical Integration using Rectangles, the Trapezoid Rule, or Simpson's Rule

Permanent Citation

Jim Brandt

"Comparing Basic Numerical Integration Methods"
http://demonstrations.wolfram.com/ComparingBasicNumericalIntegrationMethods/
Wolfram Demonstrations Project
Published: July 1, 2010