Transforming parabola to straight line

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SUMMARY

The discussion focuses on transforming the boundary of an integration domain defined by two straight lines and a parabola into a triangular shape. The equations provided are y=Ax, y=Bx, and y=(1+x)^2, where A and B are constants greater than 4. The primary goal is to maintain the straightness of the existing lines while transforming the parabola into a straight line. The user has indicated familiarity with the transformation of the parabola but prioritizes achieving straight boundaries for integration without concern for the Jacobian.

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turin
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To the moderator: This isn't a HW question, but it probably sounds like one, so I appologize. Please move this to the HW forum if need be.

I have an integration domain inside three intersecting curves. Two of the curves are straightlines and the third is a parabola. These three boundaries are of the form

<br /> y=Ax<br /> \, \qquad<br /> y=Bx<br /> \, \qquad<br /> y=(1+x)^2<br />

where A and B are arbitrary constant slopes > 4.
I want to transform the boundary of this domain into a triangle, as simply as possible. Any hints?
 
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You don't just want to turn the parabola into a straight line, you want to keep the other straight lines as straight lines as well.
 
Office_Shredder said:
You don't just want to turn the parabola into a straight line, you want to keep the other straight lines as straight lines as well.
Correct. I already know how to straighten the parabola, e.g. u=(1+x)^2; that's trivial.

BTW, I don't care about the Jacobian; my #1 priority is straight boundaries for the domain of integration.
 

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