Change of variable in a double integral

[rashida564]

Homework Statement

The image bellow is the question

Relevant Equations

Jacobian

Hi everyone, I tried to solve the last part of the question, I substituted back the expression of x and y into the equation of the ellipse, I got that r=1 or r=-1. But got no idea how to find the boundary for theta, I got a guess that, It should be from zero to pi. But got no reason why to believe this.

 

[Mark44]

Homework Statement:: The image bellow is the question
Homework Equations:: Jacobian

Hi everyone, I tried to solve the last part of the question, I substituted back the expression of x and y into the equation of the ellipse, I got that r=1 or r=-1. But got no idea how to find the boundary for theta, I got a guess that, It should be from zero to pi. But got no reason why to believe this.

After the transformation, the resulting figure is a circle of radius 1, centered at the origin. If r ranges from 0 to 1, what needs to be the range for $\theta$ to sweep out the whole circle?

 

[rashida564]

From zero to two pi, thanks man

 

[Mark44]

From zero to two pi, thanks man

Right.

BTW, I edited your post. You quoted me as saying "From zero to two pi." I didn't say this, so it's misleading to quote me.