trigonometric substitutions
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trigonometric substitutions
[¦trig·ə·nə¦me·trik ‚səb·stə′tü·shənz] (mathematics)
The substitutions x = a sin u, x = a tan u, and x = a sec u, which are used to rationalize expressions of the form √(a 2-x 2), √(x 2+ a 2), and √(x 2-a 2), respectively, when they appear in integrals.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive
If a CAS fails to give a solution here, the trigonometric substitution x=sin([theta]) converts the original integral to [integral][theta]sin([theta])d[theta], one that students should quickly recognize.
that may be rationalized with a trigonometric substitution. The integrand containing the aforementioned function of "z" is now manageable on any of the three CAS tested.
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