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!

Homework Help: Arc length, area

  1. Mar 24, 2010 #1
    1. The problem statement, all variables and given/known data
    For the curve [tex]y=\sqrt{x}[/tex] , between x = 0and x = 2, find (a) the area under the curve, (b) the arc length, (c) the volume of the solid generated when the area is revolved about the x axis, (d) the curved area of this solid.



    2. Relevant equations
    [tex]ds = \sqrt {1+(y')^{2}}dx[/tex]



    3. The attempt at a solutionI did a and c pretty easily. My problem is arc length. I wrote out the integral [tex]\int^{2}_{0} \sqrt{1+\frac{1}{4x}}dx[/tex] and realized I don't have a clue how to calculate it.

    Also, for the "curved" area. Does my professor mean surface area? How do I do that?
     
  2. jcsd
  3. Mar 24, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    To integrate that try a substitution like u^2=1+1/(4x). That will make it a rational function and then you can use partial fractions and stuff. If you don't 'know' how to solve a given integral, that's usually your first move. And the 'curved surface area' is area swept out by the curve. Look up 'surface of revolution'. There's a very similar formula to the one you have for arc length.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook