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Homework Help: Volume of a solid between 2 functions revolved about the x-axis

  1. Sep 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the volume of a solid bounded by the functions y=1-x2 and y=0 revolved around the x-axis

    2. Relevant equations (don't know how to show integrals)
    A=Pi * the integral from xa to xb of [f(x)]2-[g(x)]2

    3. The attempt at a solution
    First, to find the lower and upper x-bounds, set the functions equal to one another to get their points of intersection. You get x = 1 and -1.

    To find which function is f(x) (the greater values), pick a test point between -1 and 1. I used 0 and found 1-x2 was greater along this interval.

    So, V=Pi* the integral from -1 to 1 of (1-x2)2 dx.
    After FOIL I get 1-2x^2+x4. The integral of this polynomial is x-(2/3)x3+(1/5)x5. I then evaluated this by plugging in 1 and subtracting when I plug in -1.

    I get 16pi/15. Unsure if this is correct. Would like if someone could check my work.
  2. jcsd
  3. Sep 3, 2011 #2


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    Looks fine to me.
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