Question 1 (5 marks). Consider the region D C R defined by the equations { 1...

 

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Question 1 (5 marks). Consider the region D₁ C R² defined by the equations {¹ 1 < x² + y² < 4 0<y<x 1. (1 mark) Draw D₁.. Let R² { [R₂0 × [0, 2π] → (r, 0) → (r cos(0), r sin(0)) be the change of coordinates from the Cartesian to the polar coordinates. 2. (1 mark) What is the region D₂ CR₂0 x [0, 2] that enables to describe exactly D₁ in polar coordinates ? 3. (1 mark) What is the Jacobian determinant of on the interior of D₂ ? Let w = (x² + y²)de A dy, which is a 1-form defined on R². 4. (1 mark) Determine the pullback o*w. 5. (1 mark) Determine the integral p, using the integral f, *w. Question 1 (5 marks). Consider the region D₁ C R² defined by the equations {¹ 1 < x² + y² < 4 0<y<x 1. (1 mark) Draw D₁.. Let R² { [R₂0 × [0, 2π] → (r, 0) → (r cos(0), r sin(0)) be the change of coordinates from the Cartesian to the polar coordinates. 2. (1 mark) What is the region D₂ CR₂0 x [0, 2] that enables to describe exactly D₁ in polar coordinates ? 3. (1 mark) What is the Jacobian determinant of on the interior of D₂ ? Let w = (x² + y²)de A dy, which is a 1-form defined on R². 4. (1 mark) Determine the pullback o*w. 5. (1 mark) Determine the integral p, using the integral f, *w.

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SOLUTION 1 DISR 1 v y 4 is ty v y 1 represents ... View the full answer