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Homework Help: Relation with counting volume of a solid revolution

  1. Jan 7, 2010 #1
    1. The problem statement, all variables and given/known data

    let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2)


    3. The attempt at a solution
    i have a feeling that it has a relation with counting volume of a solid revolution.but i don't know how to answer it...
     
  2. jcsd
  3. Jan 7, 2010 #2

    tiny-tim

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    Hi b00tofuu! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Do you mean ∫02 1/(x3 + x5)2 dx ?

    If so, factor it, and then use partial fractions.
     
  4. Jan 7, 2010 #3
    Re: integral

    no, it's not what i meant...
    its the squared of the inverse function of (x^3+x^5).
    a.the question first asked about the volume of solid revolution of a function y=f(x) bounded by y=b, and the y axis. the function crossed (0,0),(a,b) where a>0. i'vc got the answer
    int(phi(f(y)^-1)^2, y = 0 .. b) by the disk method.
    then the second point of the question is where i have the problem
    b. let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2)

    i think it's related to each other... but dunno...
     
  5. Jan 7, 2010 #4

    tiny-tim

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    (please use the X2 tag just above the Reply box :wink:)

    ah, you meant ∫02 (f-1(x))2 dx.

    ok, put y = x3 + x5, then that's …

    ∫y2 dx, so substitute (something)dy for dx, change the limits, and integrate over y. :smile:
     
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