Editing 1201: Integration by Parts
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==Explanation== | ==Explanation== | ||
{{w|Integration by parts}} is an integration strategy that is used to evaluate difficult {{w|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. | {{w|Integration by parts}} is an integration strategy that is used to evaluate difficult {{w|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. | ||
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| + | Integration by parts derives from the formula for differentiating a product : ''d(u.v) = u.dv + v.du'', hence ''u.dv = d(u.v) - v.du'', and the equation can then be transposed to the integrals: '''''∫'''u.dv = [u.v] - '''∫'''v.du''. This simplifies the problem if ''u'' simplifies when differentiated, and/or ''v'' simplifies when integrated. | ||
[[Randall]] shows a somewhat complicated math problem and, in an attempt to "help", simplifies it into a more compact integral. This is the first part of performing integration by parts, which involves the guessing. Having gotten it into integration by parts format, he then leaves without describing the actual solution. The general integral '''''∫'''(u dv)'' is equal to ''uv - '''∫'''(v du)'', and this is the more tedious part of the math and where problems will arise if you picked the wrong u and dv at the beginning. The narrator makes a point of leaving here, so we can't ask for help or complain if the choice of u and dv was wrong. | [[Randall]] shows a somewhat complicated math problem and, in an attempt to "help", simplifies it into a more compact integral. This is the first part of performing integration by parts, which involves the guessing. Having gotten it into integration by parts format, he then leaves without describing the actual solution. The general integral '''''∫'''(u dv)'' is equal to ''uv - '''∫'''(v du)'', and this is the more tedious part of the math and where problems will arise if you picked the wrong u and dv at the beginning. The narrator makes a point of leaving here, so we can't ask for help or complain if the choice of u and dv was wrong. | ||
