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El_Arrow

  • one year ago

need help in finding the length of the curve

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  1. El_Arrow
    • one year ago
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    y = 2ln(sin(x/2) pi/3<x<pi

  2. El_Arrow
    • one year ago
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    i got it down to the integral of csc(x/2)

  3. El_Arrow
    • one year ago
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    @freckles @Vocaloid @amistre64 @zepdrix

  4. amistre64
    • one year ago
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    can you show your working to get to that point?

  5. El_Arrow
    • one year ago
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    yeah i'll try to draw it out

  6. El_Arrow
    • one year ago
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    |dw:1443753630087:dw|

  7. El_Arrow
    • one year ago
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    there

  8. amistre64
    • one year ago
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    sin^2 + cos^2 = 1 1 + cos^2/sin^2 = csc^2 ok, im on the same page as you now

  9. El_Arrow
    • one year ago
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    yeah thats what i did for the derivative

  10. amistre64
    • one year ago
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    an old trick is to multiply by (csc + cot) i beleive

  11. zepdrix
    • one year ago
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    Oh cosecant integral :) This is one of those annoying ones. Do you remember secant integral? it's very similar process for this one

  12. El_Arrow
    • one year ago
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    yeah i got the integral for cosecant its -ln|cscx+cotx|

  13. amistre64
    • one year ago
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    csc + cot derives to -(csc^2 + csc cot)

  14. amistre64
    • one year ago
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    the x/2 pops out tho so we need to adjust by a constant right?

  15. El_Arrow
    • one year ago
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    i guess

  16. amistre64
    • one year ago
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    -ln(cscu + cotu) (csc^2u + cscu cotu) u' -------------------- csc u + cot u u = x/2; u' = 1/2

  17. amistre64
    • one year ago
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    -2 ln ... seems fair to me

  18. El_Arrow
    • one year ago
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    wait how did you get csc^2u + cscu cotu?

  19. amistre64
    • one year ago
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    what is the derivative of csc u + cot u ?

  20. El_Arrow
    • one year ago
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    oh but shouldnt it be negative

  21. amistre64
    • one year ago
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    maybe ...

  22. El_Arrow
    • one year ago
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    why are we taking the derivative of those two if we already got the integral?

  23. amistre64
    • one year ago
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    |dw:1443754334011:dw|

  24. amistre64
    • one year ago
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    what is your question then?

  25. El_Arrow
    • one year ago
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    my question is why is my answer different from that of wolfram-alpha i got -2ln|1-2sqrt(3)|

  26. El_Arrow
    • one year ago
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    and they got -2ln|2-sqrt(3)|?

  27. El_Arrow
    • one year ago
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    i dont know if there is a step you gotta do before plugging in the integration numbers or what?

  28. amistre64
    • one year ago
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    \[-2ln(csc(pi/2)+cot(pi/2)+2ln(csc(pi/6)+cot(pi/6))\] \[2[-ln(csc(pi/2)+cot(pi/2)+ln(csc(pi/6)+cot(pi/6))\] \[2ln(\frac{csc(pi/6)+cot(pi/6)}{csc(pi/2)+cot(pi/2)})\]

  29. El_Arrow
    • one year ago
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    what the....?

  30. El_Arrow
    • one year ago
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    okay so csc(pi/6) is 2 and cot(pi/6) is sqrt(3)

  31. El_Arrow
    • one year ago
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    and csc(pi/2) is 1 and cot(pi/2) is 0

  32. El_Arrow
    • one year ago
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    so |dw:1443755083983:dw|

  33. El_Arrow
    • one year ago
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    but dont you do that only when your substracting?

  34. amistre64
    • one year ago
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    ??

  35. El_Arrow
    • one year ago
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    when do you divide the numbers when there is a natural log i mean?

  36. amistre64
    • one year ago
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    -2 ln|2-sqrt(3)| 2 ln|1/(2-sqrt(3))| 2 ln|(2+sqrt(3))/(4-3)|

  37. amistre64
    • one year ago
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    log(a) - log(b) = log(a/b) for all logs

  38. El_Arrow
    • one year ago
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    but your adding them?

  39. amistre64
    • one year ago
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    no, -2ln(b) --2ln(a) = 2ln(a)-2ln(b)

  40. amistre64
    • one year ago
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    = 2 ln(a/b)

  41. freckles
    • one year ago
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    hey where you guys at... have you guys gotten to \[2 \int\limits_\frac{\pi}{6}^\frac{\pi}{2} \csc(u) du\] if this looks funny I just subbed x/2 for u

  42. El_Arrow
    • one year ago
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    i think you have the b on top of the a

  43. amistre64
    • one year ago
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    i was trapped in OS purgatory ...

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