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hartnn

  • 2 years ago

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

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

  2. hartnn
    • 2 years ago
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    @sauravshakya @siddhantsharan

  3. hartnn
    • 2 years ago
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    @Zekarias

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

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

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

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

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

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

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

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

  12. mukushla
    • 2 years ago
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    maybe

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

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

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

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

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

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

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

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