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Find volume of solid rotated about X axis Washer method

  1. Apr 13, 2012 #1
    1. The problem statement, all variables and given/known data

    y=x^2+1
    X in (0,1)

    2. Relevant equations
    formula needed
    integral (PI [f(x)]^2 DX

    in the F(x) just plug in the equation right?

    3. The attempt at a solution
    took anti deritive of the original problem and came out with

    PI[1/3x^3+X]^2
    my answer is 5.58

    am i on the right track?

    im confused on the squared part. Do i take the Anti deritive of the squared or only the thing inside the brackets?
     
  2. jcsd
  3. Apr 13, 2012 #2
    Right, you plug f(x) into the formula, but that ^2 means you square f(x), so [f(x)]^2 = (x^2 + 1)^2. That's what you actually want to integrate.
     
  4. Apr 13, 2012 #3
    So how do i take the Anti deritive of that?

    is it 1/3(x^2+1)^3*(1/3x^3+X)^2? im going blank lol should there be a ^2 at the end of that?
     
    Last edited: Apr 13, 2012
  5. Apr 13, 2012 #4
    That wouldn't be the way to integrate it :yuck:

    Easiest way would probably be to multiply it out,
    (x2+1)2 = (x2+1)(x2+1) = ...
    then integrate each term.
     
  6. Apr 13, 2012 #5
    Got it!

    does this look right? excuse my chicken scratch handwriting.
     

    Attached Files:

  7. Apr 13, 2012 #6
    Yep, that's it!
     
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