Difference between revisions of "User:Able806/integration"
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(New page: ==Methods of Integration== ===Integration by Parts=== ===Partial Fractions=== ===Algebraic Substitution=== ===Trigonometric Substitution===) |
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===Integration by Parts=== | ===Integration by Parts=== | ||
| + | '''Integration by parts''' is a special [[Techniques of integration|technique]] to facilitate the integration of the product of two functions that otherwise lack an obvious integral. This technique utilizes the insight of the [[product rule]]. | ||
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| + | The rule for '''integration by parts''' is stated as follows: | ||
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| + | :<big><math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math></big> | ||
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| + | This rule is often useful when one function is a power of ''x'' and the other function is a trigonometric function or ''e'' raised to a power of ''x''. | ||
| + | |||
| + | Note that it may be necessary to repeat the '''integration by parts''' several times, one for each power of ''x''. | ||
| + | |||
===Partial Fractions=== | ===Partial Fractions=== | ||
===Algebraic Substitution=== | ===Algebraic Substitution=== | ||
===Trigonometric Substitution=== | ===Trigonometric Substitution=== | ||
Revision as of 13:37, April 11, 2008
Methods of Integration
Integration by Parts
Integration by parts is a special technique to facilitate the integration of the product of two functions that otherwise lack an obvious integral. This technique utilizes the insight of the product rule.
The rule for integration by parts is stated as follows:
This rule is often useful when one function is a power of x and the other function is a trigonometric function or e raised to a power of x.
Note that it may be necessary to repeat the integration by parts several times, one for each power of x.