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Homework Help: Find the Volume (Solid of Revolution)

  1. Dec 9, 2009 #1
    Find the volume of the solid y = sinx, y=cosx, and x= pi/4, revolving around x-axis



    I didn't really get this at all... do I plug pi/4 for x in y=sinx, y=cosx to get the integra boundaries?
     
    Last edited: Dec 9, 2009
  2. jcsd
  3. Dec 9, 2009 #2

    Mark44

    Staff: Mentor

    You need to give us the entire problem, including the axis this region has been revolved around.

    After that, show us what you have tried. If you're stuck, your book most likely has some similar examples that show how to calculate volumes of revolution by cylindrical shells or by washers.
     
  4. Dec 9, 2009 #3
    Sorry, forgot to mention it's revolving around the x-axis. Anyways, I got this from a friend pi * Int[0,pi/4] (cosx)^2 - (sinx)^2 dx), and I was wondering where the lower boundary, 0, came from.
     
  5. Dec 9, 2009 #4

    Mark44

    Staff: Mentor

    The description of the region that will be revolved around the x-axis is not as complete as I would like. I believe it is the region bounded by the graphs of y = sin x and y = cos x between x = 0 (the y-axis) and the line x = pi/4.

    If this is the right description, the region is sort of triangular, but with two curved sides. The "base" of this region runs along the y-axis between 0 and 1, and the two curves intersect at (pi/4, sqrt(2)/2).

    You should have at least one graph: one showing the region to be revolved, and ideally, another that shows a cross-section of the volume of revolution. Your friend is using washers - disks with a hole in the middle.

    The area of a washer is pi*(R^2 - r^2), where R is the larger radius and r is the smaller radius.

    The volume of a washer is the area time the thickness, which is pi*(R^2 - r^2)*thickness, which can be either dx (vertical washers) or dy (horizontal washers).

    For the limits of integration, figure out where the washers run. Vertical washers run left to right along the interval in question. Horizontal washers run bottom to top along the interval in question.

    Can you get started with that?
     
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