Bike Forums > Foo > Is this integral correct?
 Register All Albums Elite Membership Forum Rules Calendar Search Today's Posts Mark Forums Read

 Foo Off-Topic chit chat with no general subject.

 09-02-10, 06:57 PM #1 phantomcow2 la vache fantôme Thread Starter     Join Date: Aug 2004 Location: NH Bikes: Posts: 6,266 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) Is this integral correct? I'm trying to solve a differential equation but am stuck on a specific step that involves integration. Could someone please explain how the following is true? If we integrate both sides both sides with respect to t, I would have expected the following result: 1/(1+t^2) - 1/(1+1^2)*y = 3*arctan(t) + C And factoring out the 1/(1+t^2) from the left, we would get [1/(1+t^2)](y-1). Solving for y becomes -3*arctan(t)*(1+t^2) +1 + C = y Why am I incorrect? __________________ C://dos C://dos.run run.dos.run
 09-03-10, 08:36 AM #2 jccaclimber Senior Member   Join Date: May 2005 Location: Terre Haute, Lafayette, or Indianapolis, IN, depending on the day Bikes: n, I would like n+1 Posts: 1,918 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) I'm not 100% sure your wxy Or, xyz statement is true, but I'm not much of a math guy as far as engineers are concerned.
 09-03-10, 09:06 AM #3 jfmckenna Tiocfáidh ár Lá     Join Date: Dec 2003 Location: The edge of b# Bikes: A whole bunch-a bikes. Posts: 5,444 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 184 Post(s) This part of your equation makes no sense: 1/(1+1^2). One would simply write that as 1/2.
 09-03-10, 11:57 AM #4 jccaclimber Senior Member   Join Date: May 2005 Location: Terre Haute, Lafayette, or Indianapolis, IN, depending on the day Bikes: n, I would like n+1 Posts: 1,918 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) That second 1 is a lower case T.
 09-03-10, 12:09 PM #5 RUOkie Scarlet Knight     Join Date: May 2009 Location: In a Haggard Song Bikes: 2009 ORBEA Onix Rival. 2012 Felt Breed, 1999 Raleigh 500 Posts: 11,243 Mentioned: 22 Post(s) Tagged: 1 Thread(s) Quoted: 278 Post(s) I'm pretty sure the answer is 42 or possibly poo
09-03-10, 02:11 PM   #6
jfmckenna
Tiocfáidh ár Lá

Join Date: Dec 2003
Location: The edge of b#
Bikes: A whole bunch-a bikes.
Posts: 5,444
Mentioned: 1 Post(s)
Quoted: 184 Post(s)
Quote:
 Originally Posted by jccaclimber That second 1 is a lower case T.
Looks like a one to me but yeah must have been a typo.

 09-03-10, 03:42 PM #7 phantomcow2 la vache fantôme Thread Starter     Join Date: Aug 2004 Location: NH Bikes: Posts: 6,266 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) oops, good catch. The one should have been a lower case t. . RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number. __________________ C://dos C://dos.run run.dos.run
09-03-10, 03:46 PM   #8
banerjek
Portland Fred

Join Date: Oct 2005
Bikes: Custom Winter, Challenge Seiran SL, Fuji Team Pro, Cattrike Road/Velokit, РOS hybrid
Posts: 11,284
Mentioned: 0 Post(s)
Quoted: 74 Post(s)
Quote:
 Originally Posted by phantomcow2 RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
How can you get more general than the answer to life, the universe, and everything?

09-03-10, 03:58 PM   #9
jsharr
You Know!? For Kids!

Join Date: Apr 2005
Location: Just NW of Richardson Bike Mart
Bikes: '05 Trek 1200 / '90 Trek 8000 / '? Falcon Europa
Posts: 6,161
Mentioned: 5 Post(s)
Quoted: 14 Post(s)
Quote:
 Originally Posted by phantomcow2 oops, good catch. The one should have been a lower case t. . RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
then it has to be "poo" by process of elimination. next question please.
__________________
Are you a registered member? Why not? Click here to register. It's free and only takes 27 seconds! Help out the forums, abide by our community guidelines.
Quote:
 Originally Posted by colorider Phobias are for irrational fears. Fear of junk ripping badgers is perfectly rational. Those things are nasty.

 09-03-10, 05:07 PM #10 Greg_R Senior Member   Join Date: Jun 2008 Location: Portland, OR Bikes: Surly LHT set up for commuting Posts: 646 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) Are you asking how the last line in the image is correct? The integral of d/dt (X) with respect to t = X (integral of a derivative of X = X). That is y/1+t^2 in your example. You already agree with the right side integral solution so now you just need to multiply both sides by 1+t^2 to solve for y.