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Crazy Integral, Solution or Suggestions please!! (1 Viewer)
- Thread starter MrQuack
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turtle_2468
Member
MrQuack:
Did you get it out of a textbook, or is it just a curious q? I put it through Mathematica, and the result is distinctly non-nice. It's got elliptic functions everywhere, and I can't see a nice way to simplify it to something where I can even understand what it is: i.e. the attached pic (if it works properly)
etc. But if you found it in a textbook, then send me the answer and I can try to figure out how to get there...
Did you get it out of a textbook, or is it just a curious q? I put it through Mathematica, and the result is distinctly non-nice. It's got elliptic functions everywhere, and I can't see a nice way to simplify it to something where I can even understand what it is: i.e. the attached pic (if it works properly)
etc. But if you found it in a textbook, then send me the answer and I can try to figure out how to get there...
turtle_2468
Member
In short, no 
But you have struck the interesting point... which is that the square root of the x on the top is ruining everything. Were it just x, then taht substitution would easily work, yes...The most elegant substitution is probably x = tan u, but that still leaves non-nice square roots of trig functions over the place...
But you have struck the interesting point... which is that the square root of the x on the top is ruining everything. Were it just x, then taht substitution would easily work, yes...The most elegant substitution is probably x = tan u, but that still leaves non-nice square roots of trig functions over the place...
underthesun
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I'd love to think that this thing is outside the reach of the syllabus, but it drives me crazy thinking of the right substitution..
I still got my chem assignment to do..
I still got my chem assignment to do..
Kini Mini,
What ur talking about is if the thing was not all square root of.
then it would be easy coz we can then use logs...
BTW,
This question was some challenge question that the teacher put up on the board so....
don't kill urselves trying to solve it!!
What ur talking about is if the thing was not all square root of.
then it would be easy coz we can then use logs...
BTW,
This question was some challenge question that the teacher put up on the board so....
don't kill urselves trying to solve it!!
Mr Quack,
turtle_2468's quite right about the complexity of hte solution, put it through maple (another maths program), the answer would take two lines, with elliptical functions, etc. all over the place...
I don't know why your teacher put that as a "challenge" question... it is basically a question for the machines to play around with.....
turtle_2468's quite right about the complexity of hte solution, put it through maple (another maths program), the answer would take two lines, with elliptical functions, etc. all over the place...
I don't know why your teacher put that as a "challenge" question... it is basically a question for the machines to play around with.....
turtle_2468
Member
Hey MrQuack:
Mathematica (and maple) are immensely powerful computer programmes that integrate, differentiate, and do everything in 4U maths plus more. And they're usu v expensive, which is why they only get used in universities...
http://functions.wolfram.com/EllipticIntegrals/EllipticE/07/01/01/
gives a view of what the EllipticE function in the attached photo means.
In any case, dbl check the question your teacher gave you, but this is (after trying to simplify it) the simplest I can come up with, so there's no way it could be in the high school syllabus... (or perhaps I'm horribly wrong, but unlikely...)
good luck!
Mathematica (and maple) are immensely powerful computer programmes that integrate, differentiate, and do everything in 4U maths plus more. And they're usu v expensive, which is why they only get used in universities...
http://functions.wolfram.com/EllipticIntegrals/EllipticE/07/01/01/
gives a view of what the EllipticE function in the attached photo means.
In any case, dbl check the question your teacher gave you, but this is (after trying to simplify it) the simplest I can come up with, so there's no way it could be in the high school syllabus... (or perhaps I'm horribly wrong, but unlikely...)
good luck!
OH MY GOD...
thanks buchanan.. thats the coolest, funkiest, mega mega groovy website that I've ever been on since I've learnt intergration...
But what the hell does all the elliptical thing mean?!?! And is that an "i" i see? as in root negative 1?!?!
thanks buchanan.. thats the coolest, funkiest, mega mega groovy website that I've ever been on since I've learnt intergration...
But what the hell does all the elliptical thing mean?!?! And is that an "i" i see? as in root negative 1?!?!
turtle_2468
Member
Yes, i is sqrt negative one.
I posted a link to the EllipticE function above previously, I don't think it's simplifiable to a more "elementary" function so there goes...
btw I think that the mathematica expression you get by going to that website is more complicated than the one you're concerned with, which is in uglyexpression.doc (reason being I assumed x>0, and x real, something Mathematica doesn't take for granted!). Hope that helped.
I posted a link to the EllipticE function above previously, I don't think it's simplifiable to a more "elementary" function so there goes...
btw I think that the mathematica expression you get by going to that website is more complicated than the one you're concerned with, which is in uglyexpression.doc (reason being I assumed x>0, and x real, something Mathematica doesn't take for granted!). Hope that helped.
turtle_2468
Member
It is.