S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Thu, 20 Jun 2013 09:02:14 UTC

View unanswered posts | View active topics


Board index » High School and College Mathematics » Calculus

All times are UTC [ DST ]



Post new topic Reply to topic  Page 1 of 1
  [ 3 posts ] 
  Print view Previous topic | Next topic 
Author Message
A-R-Q
 Post subject: Evaluate the integral (3)
PostPosted: Thu, 23 Feb 2012 16:45:44 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 20 Nov 2010 21:17:02 UTC
Posts: 432
Find the indefinite integral of: e^{2x}*sin(3x) dx

Here is my attempt; apparently, I got "looped"
(ie. came back to the original question as I was going Integration by Parts...)

http://i1084.photobucket.com/albums/j40 ... MG-001.png
Top
 Profile  
 
outermeasure
 Post subject: Re: Evaluate the integral (3)
PostPosted: Thu, 23 Feb 2012 16:50:02 UTC 
Online
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6068
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
A-R-Q wrote:
Find the indefinite integral of: e^{2x}*sin(3x) dx

Here is my attempt; apparently, I got "looped"
(ie. came back to the original question as I was going Integration by Parts...)

http://i1084.photobucket.com/albums/j40 ... MG-001.png


It isn't exactly looped --- you end up with I=\text{something}+cI, where I is your integral and c\neq 1, so you have ...

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
Top
 Profile  
 
doodlenoodle
 Post subject: Re: Evaluate the integral (3)
PostPosted: Fri, 24 Feb 2012 17:29:51 UTC 
Offline
Senior Member

Joined: Sun, 12 Feb 2012 02:16:54 UTC
Posts: 64
Once you see that you have looped, you'll notice that you can just add the two, somethign liek this

integral of: e^{2x}*sin(3x) dx = something + 2/3integral of: e^{2x}*sin(3x) dx, so you can just subtract then have

integral of: e^{2x}*sin(3x) dx - 2/3integral of: e^{2x}*sin(3x) dx = something

To what the previous guy posted, :confused:
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 3 posts ] 

Board index » High School and College Mathematics » Calculus

All times are UTC [ DST ]

Who is online

Users browsing this forum: No registered users

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA