HSC Stuff > HSC Mathematics Advanced
Simpsons Rule Volume
Jefferson :
--- Quote from: jamonwindeyer on March 14, 2019, 09:52:47 am ---Hey Jefferson! I'm more in your camp here - Using Simpson's Rule in this context is flawed because the area in this case is being linearly swept, not rotated, to produce a volume. Intuitively I think of it this way - How can we give a three dimensional measurement, with absolutely no information about the third dimension? In actual practical terms, that is nonsense, and so is the way they did this question ;)
Rui is correct in that, when we do need to use Simpson's Rule for Volume, we just do it by approximating the volume integral using the formula. It's just that in this case it is a bit of a flawed exercise, because the volume we want isn't generated by rotation. This is a common thing that resources tend to get a bit wrong, I tended to just roll with it when I did my HSC :)
(An example where this works perfectly might be if we were given a vase, and radial measurements of that vase along its height, the volume integral then would be an accurate thing to do because you can think of the vase volume as a rotated area) :)
--- End quote ---
I see. That makes a lot more sense.
Thank you for clarifying!
jamonwindeyer:
--- Quote from: Jefferson on March 16, 2019, 04:41:15 pm ---I see. That makes a lot more sense.
Thank you for clarifying!
--- End quote ---
Very welcome, happy to help :)
emmajb37:
I am so lost please help!
Use simpson’s rule with 5 function values to find the volume of the solid formed when the curve y = ex is rotated about the y-axis from y = 3 to y = 5 , correct to 2 significant figures.
jamonwindeyer:
--- Quote from: emmajb37 on March 27, 2019, 08:46:12 am ---I am so lost please help!
Use simpson’s rule with 5 function values to find the volume of the solid formed when the curve y = ex is rotated about the y-axis from y = 3 to y = 5 , correct to 2 significant figures.
--- End quote ---
Hello! The first step will be to rearrange the curve, because the area is with respect to the \(y\)-axis. So:
Now, we need 5 function values between \(y=3\) and \(y=5\). So we'll do 3, 3.5, 4, 4.5, and 5. These then just get used in the Simpson's Rule formula! There are a few versions of this, here is one:
Just calculator work from there! Note you might also use the formula on the reference sheet, but you need to use that one twice (one for each half of the area) :)
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