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unscientific
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Homework Statement
The problem is to solve the integral. First I did coordinate transformation by finding jacobian = (1/4)(x2 + y2).
The problem is, I do not know the limits of integration after transformation...I tried using a graphical approach: by considering 2 cases: y>x and y<x and adding both integrals.
For y < x it is straightforward, the limits of u: [0,∞] and v: [0,∞].
However, for y > x: limits of u: [0,∞] which is easy as x,y>0 so v>0.
But the limits for v i obtained: v: [0,-∞].
When I add both integrals they sum to zero.
My suspicion is that the limits of v for y > x should be [-∞,0] and not [0,∞]. But this doesn't make sense as considering the following points:
1. y > x
2. y, x are forever increasing
Combining both, it implies " x and y are increasing with y increasing faster than x". This implies v goes from 0 to -∞..
Homework Equations
The Attempt at a Solution
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