1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arc Length and Surface question about hyperbolic function

  1. May 2, 2012 #1
    If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a

    and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of

    the curve y=cosh(x) between x=a x=-a and around the x axis.


    This is my homework question.I tried to solve it.I get a result but ı'm not sure because

    there is not number in my answer and this is area question.ı want to say my approach to

    this question.

    Firstly,ı found arc length interms of a. this is ea-e-a = 2a+4 ,i.e,
    sinh(2a)=a+2


    Secondly,ı found surface.∫2∏cosh(x)√1+sinh2(x) dx (from -a to a)

    After calculations,S=sinh(2a)+a∏/2

    Did ı do wrong something when solving the question,the answer is strange...
     
  2. jcsd
  3. May 2, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Are you sure you don't get ##2\sinh(a)## and not ##\sinh(2a)##? And it isn't that that is equal to ##2a+4##. It is the circumference of the rotated region that is equal to ##2a+4##. That may change things.
     
  4. May 2, 2012 #3
    I'm sorry,ı made a mistake by writing value.It will be 2sinh(a),but ı don't understand why it is not equal to 2a+4
     
  5. May 2, 2012 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Read the statement of the problem above.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Arc Length and Surface question about hyperbolic function
Loading...