
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 27th, 2017, 01:07 PM  #1 
Newbie Joined: Nov 2017 From: San Diego Posts: 1 Thanks: 0  How to solve this integral without Jacobian method?
How to solve this integral without Jacobian method?

November 27th, 2017, 02:42 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,460 Thanks: 489 Math Focus: Yet to find out. 
It might be useful to typeset your equations to improve readability. Could you confirm if the following translation is correct (I can't tell if that's an $n$ or an $x$ in the numerator of the exponential..)? $$\int_{2}^{1} \int_{0}^{y+2} \exp \left({\dfrac{x + y}{x  y}}\right) dx \ dy$$ 
November 28th, 2017, 04:48 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 
Looking at the integrand, I would be inclined to let u= x y. Then x= u+ y so that dx= du and x+ y= u+ 2y. When x= 0, u= y and when x= y+ 2, u= 2. The integral becomes $\displaystyle \int_{2}^{1}\int_y^2 \frac{u+ 2y}{u}dudy= \int_{2}^{1}\int_y^2 1+ 2\frac{y}{u} dudy$. 

Tags 
integral, jacobian, method, mrthod, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
double integral with Jacobian determinant  zollen  Calculus  1  July 4th, 2017 09:56 PM 
Best Method to Solve these Equations  Indigo28  Algebra  4  January 13th, 2017 02:20 PM 
Which method do I use to solve this question?  KaiL  Calculus  1  September 26th, 2015 02:13 PM 
Solve by the simplest method  chapsticks  Calculus  2  February 21st, 2012 08:58 PM 
Some method to solve any integral no matter how complex  mikfig  Calculus  2  January 8th, 2010 03:43 PM 