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appleduardo Group Title

whats the integral of arc sin x ??

  • one year ago
  • one year ago

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  1. appleduardo Group Title
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    so far i have:\[x(arcsinx)-\int\limits_{}^{}x \frac{ 1 }{ \sqrt{1-x^2} }dx\]

    • one year ago
  2. Kainui Group Title
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    Looks like you've done most of the hard part. Now take 1-x^2 and integrate by subtitution.

    • one year ago
  3. appleduardo Group Title
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    uhmm how can i do that?

    • one year ago
  4. appleduardo Group Title
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    there's where i got confused!

    • one year ago
  5. dumbcow Group Title
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    trig substitution x = sin(u) dx = cos(u) du

    • one year ago
  6. Kainui Group Title
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    So take (1-x^2)=u and take the derivative with respect to x, this becomes -2x=du/dx which can be rearranged with algebra into: xdx=-(1/2)du Substitution back into the original integrand gives: \[-\int\limits_{}^{}\frac{- du }{ 2\sqrt{u} } = \frac{ 1 }{ 2 }\int\limits_{}^{}\ u^{-1/2} du\]

    • one year ago
  7. Kainui Group Title
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    @dumbcow trig substitution isn't really useful here.

    • one year ago
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