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 June 3rd, 2013, 08:41 AM #1 Newbie   Joined: Jun 2013 Posts: 4 Thanks: 0 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.
 June 3rd, 2013, 10:16 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Finding the volume using Simpson's rule The volume in question is (using the disk method): $V=\pi\int_1\,^3 \ln^2(x)\,dx$ Thus, we want to approximate the definite integral: $I=\int_1\,^3 \ln^2(x)\,dx$ Using Simpson's rule, with $f(x)=\ln^2(x),\,n=4$ we have: $I\approx\frac{3-1}{3(4)}$$\ln^2(1)+4\ln^2\(\frac{3}{2}$$+2\ln^2(2) +4\ln^2$$\frac{5}{2}$$+\ln^2(3)\)$ Using a calculator, we find: $I\approx1.030636270916$ Hence: $V\approx\pi I\approx3.2378393372297443$
 June 3rd, 2013, 10:27 AM #3 Newbie   Joined: Jun 2013 Posts: 4 Thanks: 0 Re: Finding the volume using Simpson's rule Omg! thank you very much
 June 3rd, 2013, 10:43 AM #4 Newbie   Joined: Jun 2013 Posts: 4 Thanks: 0 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....
 June 3rd, 2013, 10:53 AM #5 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs 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
 June 3rd, 2013, 11:20 AM #6 Newbie   Joined: Jun 2013 Posts: 4 Thanks: 0 Re: Finding the volume using Simpson's rule thank you! had a typo :P

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# how to find volume using simpson's rule

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