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anonymous
 one year ago
need help in the derivation of integration formula:
anonymous
 one year ago
need help in the derivation of integration formula:

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misty1212
 one year ago
Best ResponseYou've already chosen the best response.1i didn't know there was such a formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{.}^{.} \sqrt{x^{2}a^{2}}dx =\frac{x }{ 2 }\sqrt{x ^{2}a ^{2}}\frac{ a ^{2} }{ 2 }\log \left x+\sqrt{x ^{2}+a^2} \right+C\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0solve by taking x=a sect

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no problem @misty1212

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1this one is a pain in the neck i think, but the sub is right

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1you are going to get \[a^2\int \sec^3(u)\sec(u)du\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1did you get to that part, or no?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know what to do after that.....

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1this is the kind of thing you look up in the back of the text because it is boring beyond belief

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1there is a "reduction formula" for secant

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1are you allowed to use it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0u can take the snapshot for the things u solved in the notebook instead of typing them. it could be easier, if u can do it.....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is reduction formula

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1you mean in general or "what is the reduction formula for \(\int \sec^n(x)dx\)?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1here are a bunch of them http://archives.math.utk.edu/visual.calculus/4/recursion.2/

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1in your case \(n=3\) so you get \[\int sec^3(u)du=\frac{1}{2}\tan(u)\sec(u)+\frac{1}{2}\int \sec(u)du\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hav u done it by taking integration by parts?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1it looks like that right? but it is not it comes from doing some trig business and a u sub

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1like the same trick they use for \(\int\sin^n(x)dx\) we can work through it if you like although it is not that interesting

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1oh to answer your question, no i used nothing but the"reduction formula" with \(n=3\) the one i sent the link to

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ignoring the annoying \(a^2\) out front, and combining like terms, we should be at \[\frac{a^2}{2}\sec(u)tan(u)\frac{a^2}{2}\int \sec(u)du\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know these reduction formulas...it's not in my book....in my book, the derivation was given by the method of integration by parts and in the end it was written that u can take x=sec t to solve the problem...so i did it by doing the substitution and got clutched in the middle...

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1now how to integrate secant, again it is not interesting, best to memorize it however, you want a good explanation, easier than i can write here, click on this http://math2.org/math/integrals/tableof.htm then go to "proof"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i can prove by the method of integration by parts...so no problem, when i would learn about these reduction formulas then i would go by that method also...

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1i think you use parts for \(\int \sec^3(x)dx\) but not for \(\int \sec(x)dx\)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1it is just something they do to make a formula is all some people like formulas

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1if you like partial fractions, \[\sec x =\dfrac{\cos x}{\cos^2x} = \dfrac{\cos x}{1\sin^2x}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1oh cool, lots easier than the unintuitive multiplying top and bottom business

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0please give a more detail where to start from....@ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1same can be extended to \(\sec^3x\) too i think \[\sec^3 x =\dfrac{\cos x}{\cos^4x} = \dfrac{\cos x}{(1\sin^2x)^2}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 is proving \[\int\sec(x)dx=\ln(\sec(x)+\tan(x))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know how to integrate that partial fraction....@ganeshie8

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1\[\int \frac{\cos(x)}{1\sin^2(x)}dx\] put \(u=\sin(x)\) and integrate \[\int \frac{du}{1u^2}\] using partial fractions

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 that is correct yes? never saw it done this way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yes i got that...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for \(\int\sec^3x\,dx\) i would try reduction formula though as partial fractions looks a bit lengty http://www.wolframalpha.com/input/?i=%5Cint+1%2F%281u%5E2%29%5E2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the problem is that i dont know these reduction formulas and the link that @ganeshie8 has given....i am a beginner in integration i only know the formulas given in my book....i wold rather use integration by parts from the beginning than using all such formulas...that is easiest...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the statement in the middle had initiated me...@ganeshie8
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