Numerical Integration
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.
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?
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Staff Review
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 Simpsonâs 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. -
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