Suppose you want to compute the integral of a function f : R² → R over the region S, which is bounded by the curves y = arctan x, y = - arctan x, x - y = 4, x - y = 1. y You want to use the coordinate transform given by (u, v) = h(x, y) = = 6₂ x-y). Assume you prove it is invertible on its domain. arctana We write g = h-¹. Using this transform, the integral can be written as Fill in the blanks for the bounds. Make sure to enter the bounds as simple as possible, without including any spaces etc. a= b= 3 [º [ª f(g(u, v))\ det Dg(u, v)| du du. d= No¹ but a good exercise: Find det Dg(u, v)|
Suppose you want to compute the integral of a function f : R² → R over the region S, which is bounded by the curves y = arctan x, y = - arctan x, x - y = 4, x - y = 1. y You want to use the coordinate transform given by (u, v) = h(x, y) = = 6₂ x-y). Assume you prove it is invertible on its domain. arctana We write g = h-¹. Using this transform, the integral can be written as Fill in the blanks for the bounds. Make sure to enter the bounds as simple as possible, without including any spaces etc. a= b= 3 [º [ª f(g(u, v))\ det Dg(u, v)| du du. d= No¹ but a good exercise: Find det Dg(u, v)|
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose you want to compute the integral of a function f : R² → R over the region S, which is bounded by the curves y = arctan x, y = - arctan x, x - y = 4, x - y = 1.
y
You want to use the coordinate transform given by (u, v) = h(x, y) =
= 6₂ x-y). Assume you prove it is invertible on its domain.
arctana
We write g = h-¹.
Using this transform, the integral can be written as
Fill in the blanks for the bounds.
Make sure to enter the bounds as simple as possible, without including any spaces etc.
a=
b=
3 [º [ª f(g(u, v))\ det Dg(u, v)| du du.
d=
No¹
but a good exercise: Find det Dg(u, v)|
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