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Homework Help: Check my work please?

  1. Jul 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

    2. Relevant equations



    3. The attempt at a solution

    Sometimes, I struggled with drawing a solid and a typical disc. Also, I am unsure with the solution for problem 4. Do you see any mistakes?

    I would so much appreciate your help.
     

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  3. Jul 26, 2010 #2
    This is a rare time when no one replied. Sad.
     
  4. Jul 26, 2010 #3

    Mark44

    Staff: Mentor

    You'll probably do better submitting one problem at a time.

    The first couple of problems are missing some information - namely, the line around which the region is rotated. For example, in #2, you have the region bounded by y = 1 - x2 and y = 0, but you didn't say what this region is rotated around.
     
  5. Jul 26, 2010 #4
    It's probably rotated around y = 0, especially since the problem mentions "disk and washer."

    I'm guessing the cylinder shape you drew was supposed to be a typical disk/washer the problem asked for, but that's not what you want. When the region is rotated around a horizontal line, disks and washers will be vertical, between the axis of revolution and the function for disks or between the two given functions for washers.

    On #4, what are the last three equations for?
    y = 0, x = 2, x = 4
     
  6. Jul 27, 2010 #5

    Mark44

    Staff: Mentor

    Disks and washers can be oriented either vertically or horizontally.
     
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