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Volume of the Solid bounds and integral

  1. Apr 6, 2013 #1
    Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves y= e-2x^2, y=0, x=0, x=1.

    Should the bounds for the problem be taken from the y-axis or the x-axis?

    I think that the integral for this problem would be:

    ∏∫(e-2x^2)dx , is this correct
     
    Last edited: Apr 6, 2013
  2. jcsd
  3. Apr 7, 2013 #2

    haruspex

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    That would be the same as ∏∫ydx, which is clearly wrong.
    You need to decide how you want to carve up the volume. You could do it in discs centred on the y axis, but that gets a bit messy because the integral falls into two parts (and it will involve logs). More natural is to carve it into cylinders centred on the y axis.
     
  4. Apr 7, 2013 #3
    Carving it into cylinders still uses the ∏∫R^2dx formula, right? and then my bounds would be on the y axis?
     
  5. Apr 7, 2013 #4

    haruspex

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    Yes, but what is R in this case?
    No. Each cylinder is centred on the y axis. What are its height, radius and thickness?
     
  6. Apr 7, 2013 #5
    would r be the formula but solved for x?
     
  7. Apr 9, 2013 #6

    haruspex

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    I don't know what you mean by that question. r is not much of a formula.
    If you take a slice from y = 0 to y = f(x), and from x to x+dx, in the xy plane, then rotate it around the y axis, what do you get? What is its volume? What integral would you write to add up all these volumes between x = 0 and x = 1?
     
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