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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


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    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.
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