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Thread: Simpsons rule for volume

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    YUI akuchan's Avatar
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    Simpsons rule for volume

    X_X" dunno what im doing wrong but heres the question

    The curve y = 2^x is rotated about the x-axis between x = 1 and x = 2. Use Simpsons rule with 3 function values ..find volume... 3 significant figures

    the answer is 27.2 units cubed
    while i keep gettin 17.2 units cubed, well its getting late and im getting dizzy =/ maybe thats why lol. but yeh.. its a bit hard to type up the answer without the integration symbols and stuff, but any help is appreciated

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    PC
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    Re: Simpsons rule for volume

    Use the function y = 2x to find the function values.
    These are all nice points above the x-axis, so they are effectively radii of circles, once the curve is rotated around the x-axis.

    So, now you can find the area of these three circles since you know the radii!

    Area circle 1 = πr2 = π x (21)2 = 4π
    Area circle 2 = πr2 = π x (21.5)2 = 8π
    Area circle 3 = πr2 = π x (22)2 = 16π

    Rather than use Simpson's Rule to find the area, use it to find the volume.

    Volume = h/3 x (A1 + 4A2 + A3)
    = 0.5/3 x (4π + 4 x 8π + 16n)
    = 0.5/3 x 52π
    = 27.227136333
    = 27.2 cubic units
    Last edited by PC; 8 Mar 2007 at 9:42 PM.

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    YUI akuchan's Avatar
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    Re: Simpsons rule for volume

    ohhh nice, thanks
    could someone also do it using the proper formula too
    pi [integrate]b/a y^2 dx

    its not actually b/a.. but i dunno how else to type it lol, witht hat formula, would it only work with cylinders, spheres and cones since thats where its devised from?

    also back to the simpsons rule thing, do u always find the 'area of the circles' at the function values then sub it in the formula to get the volume, before i was just subbing the y^2 into the formula and then multiply the whole thing by pi =/

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