El_Arrow
  • El_Arrow
need help in finding the length of the curve
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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El_Arrow
  • El_Arrow
y = 2ln(sin(x/2) pi/3
El_Arrow
  • El_Arrow
i got it down to the integral of csc(x/2)
El_Arrow
  • El_Arrow
@freckles @Vocaloid @amistre64 @zepdrix

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amistre64
  • amistre64
can you show your working to get to that point?
El_Arrow
  • El_Arrow
yeah i'll try to draw it out
El_Arrow
  • El_Arrow
|dw:1443753630087:dw|
El_Arrow
  • El_Arrow
there
amistre64
  • amistre64
sin^2 + cos^2 = 1 1 + cos^2/sin^2 = csc^2 ok, im on the same page as you now
El_Arrow
  • El_Arrow
yeah thats what i did for the derivative
amistre64
  • amistre64
an old trick is to multiply by (csc + cot) i beleive
zepdrix
  • zepdrix
Oh cosecant integral :) This is one of those annoying ones. Do you remember secant integral? it's very similar process for this one
El_Arrow
  • El_Arrow
yeah i got the integral for cosecant its -ln|cscx+cotx|
amistre64
  • amistre64
csc + cot derives to -(csc^2 + csc cot)
amistre64
  • amistre64
the x/2 pops out tho so we need to adjust by a constant right?
El_Arrow
  • El_Arrow
i guess
amistre64
  • amistre64
-ln(cscu + cotu) (csc^2u + cscu cotu) u' -------------------- csc u + cot u u = x/2; u' = 1/2
amistre64
  • amistre64
-2 ln ... seems fair to me
El_Arrow
  • El_Arrow
wait how did you get csc^2u + cscu cotu?
amistre64
  • amistre64
what is the derivative of csc u + cot u ?
El_Arrow
  • El_Arrow
oh but shouldnt it be negative
amistre64
  • amistre64
maybe ...
El_Arrow
  • El_Arrow
why are we taking the derivative of those two if we already got the integral?
amistre64
  • amistre64
|dw:1443754334011:dw|
amistre64
  • amistre64
what is your question then?
El_Arrow
  • El_Arrow
my question is why is my answer different from that of wolfram-alpha i got -2ln|1-2sqrt(3)|
El_Arrow
  • El_Arrow
and they got -2ln|2-sqrt(3)|?
El_Arrow
  • El_Arrow
i dont know if there is a step you gotta do before plugging in the integration numbers or what?
amistre64
  • amistre64
\[-2ln(csc(pi/2)+cot(pi/2)+2ln(csc(pi/6)+cot(pi/6))\] \[2[-ln(csc(pi/2)+cot(pi/2)+ln(csc(pi/6)+cot(pi/6))\] \[2ln(\frac{csc(pi/6)+cot(pi/6)}{csc(pi/2)+cot(pi/2)})\]
El_Arrow
  • El_Arrow
what the....?
El_Arrow
  • El_Arrow
okay so csc(pi/6) is 2 and cot(pi/6) is sqrt(3)
El_Arrow
  • El_Arrow
and csc(pi/2) is 1 and cot(pi/2) is 0
El_Arrow
  • El_Arrow
so |dw:1443755083983:dw|
El_Arrow
  • El_Arrow
but dont you do that only when your substracting?
amistre64
  • amistre64
??
El_Arrow
  • El_Arrow
when do you divide the numbers when there is a natural log i mean?
amistre64
  • amistre64
-2 ln|2-sqrt(3)| 2 ln|1/(2-sqrt(3))| 2 ln|(2+sqrt(3))/(4-3)|
amistre64
  • amistre64
log(a) - log(b) = log(a/b) for all logs
El_Arrow
  • El_Arrow
but your adding them?
amistre64
  • amistre64
no, -2ln(b) --2ln(a) = 2ln(a)-2ln(b)
amistre64
  • amistre64
= 2 ln(a/b)
freckles
  • freckles
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
El_Arrow
  • El_Arrow
i think you have the b on top of the a
amistre64
  • amistre64
i was trapped in OS purgatory ...

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