June 29th, 2012, 12:25 AM  #1 
Newbie Joined: Jun 2012 Posts: 13 Thanks: 0  Integral  compare solution
I have one integral and I would like comparing solution with you 
June 29th, 2012, 01:13 AM  #2 
Newbie Joined: Jun 2012 Posts: 13 Thanks: 0  Re: Integral  compare solution
This is my solution and this is Mathematica 
June 29th, 2012, 02:43 AM  #3 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Integral  compare solution
Your answer needs to be halved. If you have doubts about any result, check with differentiation and then try graphing it. There are many ways in which an antiderivative can turn out, especially when you remember the constant may differ. For example, I got , which is just the same function if x is real. 
June 29th, 2012, 03:17 AM  #4 
Newbie Joined: Jun 2012 Posts: 13 Thanks: 0  Re: Integral  compare solution
I know that may be multisolution depend of way of integration. Graphical method is good but in case where we don't have calculator or program may be serious problem. In any cases I thank to you for effort in discovering solution. 
June 29th, 2012, 06:08 PM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Integral  compare solution Hello,debad! aswoods is correct . . . You need a 2 in the denominator. Quote:
Your answer can be simplified . . . [color=beige]. . [/color]  
June 30th, 2012, 04:15 AM  #6 
Senior Member Joined: May 2011 Posts: 501 Thanks: 5  Re: Integral  compare solution
Often times, math engines such as Maple and Mathematica will give unsimplified solutions. One can simplify them down by using 'simplify'. I have Maple, and often I have to use 'simplify(%)' to get it down to a reasonable looking solution. I am not sure what the code is in Mathematica. 
June 30th, 2012, 10:33 AM  #7 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Integral  compare solution
I noticed that the quality of Wolfram Alpha isn't very good. Although it can solve some problems nothing else can (when it chooses to), it's terrible at simplifying those answers. It used to have problems simplifying log(e).

June 30th, 2012, 11:50 AM  #8  
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Integral  compare solution Quote:
 
June 30th, 2012, 03:45 PM  #9 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Integral  compare solution
You have to remember that it tries to produce an answer that is valid for as many arguments as possible. For complex arguments, many obvious simplifications ignore whatever branch cuts are in use and so may result in a strictly incorrect answer. In many cases it should show underneath a simplified version "for real x" or "for positive x".

July 1st, 2012, 03:18 AM  #10  
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Integral  compare solution Quote:
For example Code: Assuming[x>0,Integrate[Sqrt[x],x]]  

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