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hartnn
 2 years ago
Efficient (or any) way to integrate this:
\(\large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)
hartnn
 2 years ago
Efficient (or any) way to integrate this: \(\large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)

This Question is Closed

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2\(\huge \int \large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2@sauravshakya @siddhantsharan

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0did you try competing square?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2adding and subtracting 2ab sinxcosx ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0yep thats what came into my ind first not foolproof

Zekarias
 2 years ago
Best ResponseYou've already chosen the best response.0what if we insert 1sin^2(x) instead of cos^2(x)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2\(\sqrt{(acos x+bsinx)^22absinxcosx}\) hmm....what next ?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.4seems to be an elliptic integral and there is no closed form for elliptic integrals

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2yes, i heard same thing earlier....but could not digest that this simple function is not integrable......

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2no closed form...any *open* form ?

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0You may try the Weierstrass substitution....

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.4more simpler\[\int \sqrt{1+\sin^2 x} \ \text{d}x\]but no closed form :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2ohh...okk....so no closed form means? do we write it in some new function form ?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.4closed form means there is no antiderivative for integrand in terms of elementary functions

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2ok,then.....no use banging our heads,solving this....m closing it.....
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