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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?
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November 27th, 2017, 02:42 PM   #2
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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..)?

$$\int_{-2}^{-1} \int_{0}^{y+2} \exp \left({\dfrac{x + y}{x - y}}\right) dx \ dy$$
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November 28th, 2017, 04:48 AM   #3
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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
$\displaystyle \int_{-2}^{-1}\int_y^2 \frac{u+ 2y}{u}dudy= \int_{-2}^{-1}\int_y^2 1+ 2\frac{y}{u} dudy$.
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