Editing 1201: Integration by Parts
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| title = Integration by Parts | | title = Integration by Parts | ||
| image = integration by parts.png | | image = integration by parts.png | ||
− | | titletext = If you can manage to choose u and v such that u = v = x, then the answer is just (1/2) | + | | titletext = If you can manage to choose u and v such that u = v = x, then the answer is just (1/2)x^2, which is easy to remember. Oh, and add a '+C' or you'll get yelled at. |
}} | }} | ||
==Explanation== | ==Explanation== | ||
− | {{w|Integration by parts}} is an integration strategy that is used to evaluate difficult | + | {{w|Integration by parts}} is an integration strategy that is used to evaluate difficult integrals by trying to find simpler integrals derived from the original. It is commonly a source of confusion or irritation for students when they first learn it, due to the fact that there is really no way to accurately predict the proper u/dv separation just by looking at an integral. Integration by parts requires patience, trial and error, and experience. |
− | + | Randall shows a somewhat complicated math problem and, in an attempt to "help", simplifies it into a more compact integral. Having gotten it into integration by parts format, he then leaves, so we can't ask for help or complain. This is the point where students often get stuck. | |
− | + | In the title text, he points out that the integral of x can be divided so that u = x and dv = dx (implying v = x), which leads to the result (1/2)x^2. Mathematics teachers and extreme math geeks will cringe at this answer, however, since an indefinite integral requires an integration constant. The correct answer is actually (1/2)x^2 + C, as Randall hints. | |
==Transcript== | ==Transcript== | ||
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{{comic discussion}} | {{comic discussion}} | ||
− | [[Category: | + | [[Category:Math]] |
[[Category:Sarcasm]] | [[Category:Sarcasm]] |