1 / 4

7.7 Approximate Integration

7.7 Approximate Integration. If we wish to evaluate a definite integral involving a function whose antiderivative we cannot find, then we must resort to an approximation technique. We describe three such techniques in this section. Midpoint Rule Trapezoidal Rule Simpson’s Rule. y.

libitha
Download Presentation

7.7 Approximate Integration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7.7 Approximate Integration If we wish to evaluate a definite integral involving a function whose antiderivative we cannot find, then we must resort to an approximation technique. We describe three such techniques in this section. • Midpoint Rule • Trapezoidal Rule • Simpson’s Rule

  2. y A. Midpoint Rule Let f be continuous on [a, b]. The Midpoint Rule for approximating is given by x a … b B. Trapezoidal Rule y Let f be continuous on [a, b]. The Trapezoidal Rule for approximating is given by x … C. Simpson’s Rule (n is even) y Let f be continuous on [a, b]. The Simpson’s Rule for approximating is given by x …

  3. Example 1: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) the Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) (a) Trapezoidal Rule (b) Midpoint Rule (c) Simpson’s Rule

  4. Example 2: The width (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Use Simpson’s Rule to estimate the area of the pool. 6.8 5.6 5.0 7.2 4.8 4.8 6.2 Solutions: Let x = distance from the left end of the pool w = w(x) = width at x

More Related