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Homework Help: Volume of the Solid involving Hyperbolic functions

  1. Jun 1, 2010 #1
    1. The problem statement, all variables and given/known data

    The area bounded by y=2 coshx, the x-axis, the y-axis, and the line x=4 is revolved about the x-axis. Find the volume of the solid generated.

    2. Relevant equations

    I sliced the area along the axis of revolution. That is the strip is dx. So the equation necessary is pi(R^2-r^2) from the limits of integration (0,4)

    3. The attempt at a solution
    pi[tex]\int((2cosh(x))^2-16)[/tex] from 0 to 4
    I am uncertain if my logic is sound. Any feedback would be appreciated.
  2. jcsd
  3. Jun 1, 2010 #2
    I think it would be best to use disks to solve this problem. If I were to use shells the slicing would be awkward. Can anyone give me some pointers?
  4. Jun 2, 2010 #3


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    Gold Member

    Why not just integrate pi*(2*cosh(x))^2 dx from 0 to 4

    Your vertical strip is just between y=2*cosh(x) and y=0. So pi(R^2-0). x=4 is just the boundary condition, your limits are from x=0 to x=4
    Last edited: Jun 2, 2010
  5. Jun 2, 2010 #4
    Thank you. The thought occurred to me that I could just integrate that. And the logic behind that seems sound by my accounts. I just needed some additional feedback.
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