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PinkPocky
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Calculus: Coordinate Changes, Jacobian, Double Integrals??
Show that T(u,v) = (u2 - v2, 2uv)
maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D,
bounded by x=0, y=0, and y2 = 324 - 36x.
Use T to calculate ∬sqrt(x2+y2) dxdy on the region D.
I know that dxdy = the Jacobian = (4u2+4v2)dudv.
I'm have a really hard time finding a way to figure what the bounds of the integral are, in terms of u and v.
Homework Statement
Show that T(u,v) = (u2 - v2, 2uv)
maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D,
bounded by x=0, y=0, and y2 = 324 - 36x.
Use T to calculate ∬sqrt(x2+y2) dxdy on the region D.
Homework Equations
The Attempt at a Solution
I know that dxdy = the Jacobian = (4u2+4v2)dudv.
I'm have a really hard time finding a way to figure what the bounds of the integral are, in terms of u and v.