
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 xaxis 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 xaxis. 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): Thus, we want to approximate the definite integral: Using Simpson's rule, with we have: Using a calculator, we find: Hence: 
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 TI89 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


Tags 
finding, rule, simpson, volume 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Simpson's Rule  aaronmath  Calculus  1  October 2nd, 2011 11:36 PM 
Simpson's Rule  aaronmath  Calculus  1  September 30th, 2011 05:45 AM 
I have a trouble about Simpson's rule  khyratmath123  Algebra  4  March 24th, 2010 08:13 AM 
simpson's 1/3rd rule  rakeshkool27  Calculus  4  March 21st, 2010 04:35 PM 
Simpson's Rule  igodspeed  Calculus  1  March 4th, 2009 12:53 AM 