Question about finding area using Green's Theorem

[Mohamed Abdul]

Homework Statement

Use Green's Theorem to find the area of the region between the x-axis and the curve parameterized by r(t)=<t-sin(t), 1-cos(t)>, 0 <= t <= 2pi

Attached is a figure pertaining to the question

Homework Equations

[/B]

The Attempt at a Solution

Using the parameterized curve, I have been able to locate the x boundaries between 0 and 2pi and the y boundaries between 0 and 1-cos(t). However, I do not know how to proceed with the double integral because I don't have the vector field equation. Can anyone help me out?

 

[Ray Vickson]

Homework Statement

Use Green's Theorem to find the area of the region between the x-axis and the curve parameterized by r(t)=<t-sin(t), 1-cos(t)>, 0 <= t <= 2pi

Attached is a figure pertaining to the question

View attachment 214363

Homework Equations

View attachment 214364 [/B]

The Attempt at a Solution

Using the parameterized curve, I have been able to locate the x boundaries between 0 and 2pi and the y boundaries between 0 and 1-cos(t). However, I do not know how to proceed with the double integral because I don't have the vector field equation. Can anyone help me out?

You want to end up with an integral of the form
$$ \int \int_D 1 \, dA, $$
so what does that tell you about $P$ and $Q$?

 

[Mohamed Abdul]

You want to end up with an integral of the form
$$ \int \int_D 1 \, dA, $$
so what does that tell you about $P$ and $Q$?

Would P and Q just be 1 in that case?

 

[Ray Vickson]

Would P and Q just be 1 in that case?

You tell me. Do you get the right value of $\partial Q/ \partial x - \partial P / \partial y$?