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Homework Help: Can some 1 do this

  1. Apr 7, 2005 #1
    Find the volume of the solid formed with a base bounded by y = (x^2)-2 and y=4 filled with squares that are perpendicualr to the x-axis.
  2. jcsd
  3. Apr 7, 2005 #2
    .....i think you can find that area using simpson's rule , you can thus proceed to find the volume using the maximum height............yeah i think that should work....
  4. Apr 9, 2005 #3
    It's really not necessary to use Simpson's Rule. Find an volume by cross-section. In order to do that, you need to develop an equation for the area, in this case a square. By the equations you gave, the length of one side of the square would be [tex]4-[(x^2)-2][/tex]. Since the cross-sections are perpendicular to the x axis. You can leave the function as is since it is already in terms of x. So the formula for volume by cross-sections is

    [tex]\int^a_b A(x)\delta x[/tex]

    so after finding your a and b, (set the equations equal to each other)

    you get the [tex]\int^2_{-2} {4-[x^2-2)]}^2 \delta x=16[/tex]
    Last edited: Apr 9, 2005
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