## El_Arrow one year ago need help in finding the length of the curve

1. El_Arrow

y = 2ln(sin(x/2) pi/3<x<pi

2. El_Arrow

i got it down to the integral of csc(x/2)

3. El_Arrow

@freckles @Vocaloid @amistre64 @zepdrix

4. amistre64

can you show your working to get to that point?

5. El_Arrow

yeah i'll try to draw it out

6. El_Arrow

|dw:1443753630087:dw|

7. El_Arrow

there

8. amistre64

sin^2 + cos^2 = 1 1 + cos^2/sin^2 = csc^2 ok, im on the same page as you now

9. El_Arrow

yeah thats what i did for the derivative

10. amistre64

an old trick is to multiply by (csc + cot) i beleive

11. zepdrix

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

yeah i got the integral for cosecant its -ln|cscx+cotx|

13. amistre64

csc + cot derives to -(csc^2 + csc cot)

14. amistre64

the x/2 pops out tho so we need to adjust by a constant right?

15. El_Arrow

i guess

16. amistre64

-ln(cscu + cotu) (csc^2u + cscu cotu) u' -------------------- csc u + cot u u = x/2; u' = 1/2

17. amistre64

-2 ln ... seems fair to me

18. El_Arrow

wait how did you get csc^2u + cscu cotu?

19. amistre64

what is the derivative of csc u + cot u ?

20. El_Arrow

oh but shouldnt it be negative

21. amistre64

maybe ...

22. El_Arrow

why are we taking the derivative of those two if we already got the integral?

23. amistre64

|dw:1443754334011:dw|

24. amistre64

what is your question then?

25. El_Arrow

my question is why is my answer different from that of wolfram-alpha i got -2ln|1-2sqrt(3)|

26. El_Arrow

and they got -2ln|2-sqrt(3)|?

27. El_Arrow

i dont know if there is a step you gotta do before plugging in the integration numbers or what?

28. amistre64

$-2ln(csc(pi/2)+cot(pi/2)+2ln(csc(pi/6)+cot(pi/6))$ $2[-ln(csc(pi/2)+cot(pi/2)+ln(csc(pi/6)+cot(pi/6))$ $2ln(\frac{csc(pi/6)+cot(pi/6)}{csc(pi/2)+cot(pi/2)})$

29. El_Arrow

what the....?

30. El_Arrow

okay so csc(pi/6) is 2 and cot(pi/6) is sqrt(3)

31. El_Arrow

and csc(pi/2) is 1 and cot(pi/2) is 0

32. El_Arrow

so |dw:1443755083983:dw|

33. El_Arrow

but dont you do that only when your substracting?

34. amistre64

??

35. El_Arrow

when do you divide the numbers when there is a natural log i mean?

36. amistre64

-2 ln|2-sqrt(3)| 2 ln|1/(2-sqrt(3))| 2 ln|(2+sqrt(3))/(4-3)|

37. amistre64

log(a) - log(b) = log(a/b) for all logs

38. El_Arrow

39. amistre64

no, -2ln(b) --2ln(a) = 2ln(a)-2ln(b)

40. amistre64

= 2 ln(a/b)

41. 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

42. El_Arrow

i think you have the b on top of the a

43. amistre64

i was trapped in OS purgatory ...