MHB Change of variables/ Transformations

[Joe20]

I have obtained as such using changing of variables/ transformations:

Let u= y/x and v= xy after manipulating the equation of the curves as such xy = 5, xy = 2, y/x = 1 and y/x = 4.
Then u = 1, u = 4, v = 5 and v = 2 => obtain a square on the u-v plane.

Change the integrand to:

Outer integral: 2 to 5
inner integral: 1 to 4
replace the expression for y/x to u [ u cos (u\pi) du dv]

I am not sure if I have done it correctly thus far. If so, how do i integrate that expression? Need advice.

 

[tkhunny]

I have obtained as such using changing of variables/ transformations:

Let u= y/x and v= xy after manipulating the equation of the curves as such xy = 5, xy = 2, y/x = 1 and y/x = 4.
Then u = 1, u = 4, v = 5 and v = 2 => obtain a square on the u-v plane.

Change the integrand to:

Outer integral: 2 to 5
inner integral: 1 to 4
replace the expression for y/x to u [ u cos (u\pi) du dv]

I am not sure if I have done it correctly thus far. If so, how do i integrate that expression? Need advice.

Seems to me you'll be needing the Jacobian in your new integral. I'm hoping this isn't the first you've heard of it.

 

[Joe20]

Seems to me you'll be needing the Jacobian in your new integral. I'm hoping this isn't the first you've heard of it.

Hi Yes I will need to multiply by the jacobian value which I have missed out. (anyway that suppose to be a constant). Would like to know how should I integrate such expression from what I have stated.

 

[tkhunny]

Hi Yes I will need to multiply by the jacobian value which I have missed out. (anyway that suppose to be a constant). Would like to know how should I integrate such expression from what I have stated.

No objection to anything else I see. You had better PROVE that it's a constant.