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hartnn Group Title

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

  • 2 years ago
  • 2 years ago

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  1. hartnn Group Title
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    \(\huge \int \large \sqrt{a^2cos^2 x+b^2sin^2x}dx\)

    • 2 years ago
  2. hartnn Group Title
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    @sauravshakya @siddhantsharan

    • 2 years ago
  3. hartnn Group Title
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    @Zekarias

    • 2 years ago
  4. AravindG Group Title
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    did you try competing square?

    • 2 years ago
  5. hartnn Group Title
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    adding and subtracting 2ab sinxcosx ?

    • 2 years ago
  6. AravindG Group Title
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    yep thats what came into my ind first not foolproof

    • 2 years ago
  7. hartnn Group Title
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    plz.,try...

    • 2 years ago
  8. AravindG Group Title
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    did that work @hartnn

    • 2 years ago
  9. Zekarias Group Title
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    what if we insert 1-sin^2(x) instead of cos^2(x)

    • 2 years ago
  10. hartnn Group Title
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    \(\sqrt{(acos x+bsinx)^2-2absinxcosx}\) hmm....what next ?

    • 2 years ago
  11. mukushla Group Title
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    seems to be an elliptic integral and there is no closed form for elliptic integrals

    • 2 years ago
  12. mukushla Group Title
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    maybe

    • 2 years ago
  13. hartnn Group Title
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    yes, i heard same thing earlier....but could not digest that this simple function is not integrable......

    • 2 years ago
  14. hartnn Group Title
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    no closed form...any *open* form ?

    • 2 years ago
  15. estudier Group Title
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    You may try the Weierstrass substitution....

    • 2 years ago
  16. mukushla Group Title
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    more simpler\[\int \sqrt{1+\sin^2 x} \ \text{d}x\]but no closed form :)

    • 2 years ago
  17. hartnn Group Title
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    ohh...okk....so no closed form means? do we write it in some new function form ?

    • 2 years ago
  18. mukushla Group Title
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    closed form means there is no antiderivative for integrand in terms of elementary functions

    • 2 years ago
  19. hartnn Group Title
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    ok,then.....no use banging our heads,solving this....m closing it.....

    • 2 years ago
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