My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 2nd, 2017, 03:34 PM   #1
Senior Member
 
Joined: Jan 2017
From: Toronto

Posts: 140
Thanks: 2

changing of variables and determining the boundaries

Evaluate

$\displaystyle
\int \int (x+y) e^{x-y}
$

over the triangle with corners (0, 0), (-1, 1), and (1, 1),
using x = (u + v)/2, y = (u - v)/2

Is there any systematic method to determine the new boundaries of u and v?

Last edited by zollen; August 2nd, 2017 at 04:30 PM.
zollen is offline  
 
August 2nd, 2017, 04:26 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,488
Thanks: 749

you lost me at

$x = (u+v)=2, ~y=(u-v)=2$

do you mean

$x = \dfrac{u+v}{2},~y = \dfrac{u-v}{2}$ ?
romsek is offline  
August 2nd, 2017, 04:30 PM   #3
Senior Member
 
Joined: Jan 2017
From: Toronto

Posts: 140
Thanks: 2

Sorry, I just fixed my first post.
zollen is offline  
August 2nd, 2017, 05:20 PM   #4
Senior Member
 
Joined: Jan 2017
From: Toronto

Posts: 140
Thanks: 2

You may have forgotten the Jacobian. No matter. You have already answered my question.
zollen is offline  
August 2nd, 2017, 05:58 PM   #5
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,488
Thanks: 749

Quote:
Originally Posted by zollen View Post
You may have forgotten the Jacobian. No matter. You have already answered my question.
I did, which is why I deleted the post. I wasn't getting the same answer from both integrations.

But as you noticed they were off by a factor of 2 which is the determinant of the Jacobian, which in this case is just the transform matrix.
romsek is offline  
August 2nd, 2017, 08:46 PM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 18,037
Thanks: 1394

The triangle's vertices will be given by (u, v) = (0, 0), (0, -2) and (2, 0). The u-axis and the v-axis are perpendicular. Make a rough sketch.
skipjack is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
boundaries, changing, determining, variables



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Side Boundaries GabrielT Calculus 2 March 21st, 2017 08:42 AM
boundaries alexmath Calculus 2 May 27th, 2012 06:05 PM
CONFIDENCE LEVEL and BOUNDARIES - please help oliver1 Advanced Statistics 1 March 21st, 2012 09:29 PM
A little help with boundaries plitter Calculus 0 January 13th, 2009 06:17 AM
Determining bounds when changing variables isaace Calculus 6 November 28th, 2008 12:59 PM





Copyright © 2017 My Math Forum. All rights reserved.