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Is this the right integral set-up to find the volume?

  1. Feb 3, 2013 #1
    1. Find volume between f(x) = x, g(x)= sin(sqrt(5x+3)), x=1, and x=2, when revolved around y=4.


    2. Would it be correct to write the integral like this?

    ∫1 to 2 of [[itex]\pi[/itex](4 - sin(√(5x + 3))2 - [itex]\pi[/itex](4 - x)2]


    I am using the washer method, and for the gap that's in the middle I usually think about it by saying r= inner curve - axis of rotation.
    R= outer curve - axis of rotation

    But in this case the axis of rotation is above the function, so would it be r= 4 - inner curve

    and R= 4 - outer curve?

    Thanks! :)
     
  2. jcsd
  3. Feb 3, 2013 #2
    Please answer! :cry:
     
  4. Feb 3, 2013 #3

    haruspex

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    Yes, that's right. You ought to check that the curves do not cross within the range.
     
  5. Feb 3, 2013 #4
    Yes, the inner radius should be 4 - inner curve and the outer radius should be 4 - outer curve. I think your setup is correct.
     
  6. Feb 3, 2013 #5
    :D Thanks so much, haruspex and JPaquim! :D
     
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