# Numerical Integration

Taught by Houston
• Currently 4.0/5 Stars.
3797 views | 5 ratings
Meets NCTM Standards:
Lesson Summary:

In this lesson on numerical integration, we learn how to approximate a definite integral using only a finite number of function values at equally spaced points in the interval. We start with the trapezoid rule, which uses the area of a trapezoid to approximate the area under the curve. We then move on to Simpson's rule, which approximates the area under the curve with the area under a parabola. Both methods have error estimates that allow us to determine the accuracy of our approximation.

Lesson Description:

Trapezoid Rule and Simpson's Rule. Error estimates.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

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• What is numerical integration?
• How do you estimate an integral numerically?
• What is the trapezoid rule for approximating an integral?
• How do you estimate an integral to within 0.0005?
• What is Simpson's Rule?
• What is the 3-point Simpson Rule?
• What is the composite Simpson Rule?
• How do you compute S4 for the integral of 1/(1 + ln x) between 1 and 3?
• How do you estimate error for Simpson's Rule?
• How do you find n so that Sn is guaranteed to be accurate to within 0.00005?
• How do you do the trapezoid rule on a calculator?
• How do you do Simpson's Rule on a calculator?
• #### Staff Review

• Currently 4.0/5 Stars.
This is a really thorough explanation of estimating integrals numerically using trapezoids. It is also possible to determine what the error in the calculation will be. Also discussed is Simpsonâs Rule, how to make calculations to estimate integrals, and what the error estimate is for the rule. A good explanation of what can be a very complicated process in Calculus.
• #### mohamd

• Currently 5.0/5 Stars.
nice vid
• #### yoleven

• Currently 5.0/5 Stars.
Very clear and thorough. Well done!