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November 27th, 2017, 01:07 PM   #1
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How to solve this integral without Jacobian method?

How to solve this integral without Jacobian method?
Attached Images 0A410393-9EDB-41E7-931F-4AAE0C3A9ACC.jpg (19.8 KB, 3 views) November 27th, 2017, 02:42 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,849 Thanks: 661 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: 3,264 Thanks: 902 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post zollen Calculus 1 July 4th, 2017 09:56 PM Indigo28 Algebra 4 January 13th, 2017 02:20 PM KaiL Calculus 1 September 26th, 2015 02:13 PM chapsticks Calculus 2 February 21st, 2012 08:58 PM mikfig Calculus 2 January 8th, 2010 03:43 PM

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