hartnn
  • hartnn
Efficient (or any) way to integrate this: \(\large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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hartnn
  • hartnn
\(\huge \int \large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)
hartnn
  • hartnn
@sauravshakya @siddhantsharan
hartnn
  • hartnn
@Zekarias

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More answers

AravindG
  • AravindG
did you try competing square?
hartnn
  • hartnn
adding and subtracting 2ab sinxcosx ?
AravindG
  • AravindG
yep thats what came into my ind first not foolproof
hartnn
  • hartnn
plz.,try...
AravindG
  • AravindG
did that work @hartnn
anonymous
  • anonymous
what if we insert 1-sin^2(x) instead of cos^2(x)
hartnn
  • hartnn
\(\sqrt{(acos x+bsinx)^2-2absinxcosx}\) hmm....what next ?
anonymous
  • anonymous
seems to be an elliptic integral and there is no closed form for elliptic integrals
anonymous
  • anonymous
maybe
hartnn
  • hartnn
yes, i heard same thing earlier....but could not digest that this simple function is not integrable......
hartnn
  • hartnn
no closed form...any *open* form ?
anonymous
  • anonymous
You may try the Weierstrass substitution....
anonymous
  • anonymous
more simpler\[\int \sqrt{1+\sin^2 x} \ \text{d}x\]but no closed form :)
hartnn
  • hartnn
ohh...okk....so no closed form means? do we write it in some new function form ?
anonymous
  • anonymous
closed form means there is no antiderivative for integrand in terms of elementary functions
hartnn
  • hartnn
ok,then.....no use banging our heads,solving this....m closing it.....

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