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June 3rd, 2013, 08:41 AM   #1
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Finding the volume using Simpson's rule

Okay, so I've literally tried everything on this question and I cant seem the get the right answer...

The diagram shows part of the curve with equation y=ln(x).
The region bounded by the curve y=ln(x), the x-axis and the line x=3 is shaded (basically its the graph y=ln(x) between x=3 and where x=1 is shaded)

a) The shaded region is rotated through 360 degrees about the x-axis. Use Simpson's Rule with five ordinates (4 strips) to find an approximation for the volume of the solid generated, give answer to 4 s.f.

The answer is 3.238 (4.s.f) btw.

Thanks.
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June 3rd, 2013, 10:16 AM   #2
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Re: Finding the volume using Simpson's rule

The volume in question is (using the disk method):



Thus, we want to approximate the definite integral:



Using Simpson's rule, with we have:



Using a calculator, we find:



Hence:

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June 3rd, 2013, 10:27 AM   #3
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Re: Finding the volume using Simpson's rule

Omg! thank you very much
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June 3rd, 2013, 10:43 AM   #4
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Re: Finding the volume using Simpson's rule

wait how do you type e.g. ln^2(1.5) into the calculator? (ln1.5)^2 ? casue when i plug everything into the my caluclator i get a different asnwer, i get 2.4049 instead of 1.0306....
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June 3rd, 2013, 10:53 AM   #5
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Re: Finding the volume using Simpson's rule

I entered the command:

(1/6)(ln^2(1)+4ln^2(3/2)+2ln^2(2)+4ln^2(5/2)+ln^2(3))

at http://www.wolframalpha.com

On my TI-89 Titanium, the command:

(1/6)((ln(1))^2+4(ln(1.5))^2+2(ln(2))^2+4(ln(2.5))^2+ (ln(3))^2) [ENTER]

returns:

1.03063627092
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June 3rd, 2013, 11:20 AM   #6
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Re: Finding the volume using Simpson's rule

thank you! had a typo :P
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