Calculating Area of Curve Using Greens Theorem

[bugatti79]

Homework Statement

Find area of curve using area formula of Greens theorem

Homework Equations

r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi. The curve is y = sin x

The Attempt at a Solution

Do i let x(t)=t...?

 

[spaghetti3451]

I have no idea what you mean by 'The curve is y = sin x.'

I am assuming that the region is defined by 'r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi'. If so, the area is given by the line integral of 0.5xdy - 0.5ydx, where x = t - sin t and y = 1 - cos t.

Why not solve the problem and post your answer and any further queries you might have about the problem?

Once you have finished, I will tell you why the line integral of 0.5xdy - 0.5ydx turns out to be the formula for Green's Theorem.

 

[SammyS]

Homework Statement

Find area of curve using area formula of Greens theorem

Homework Equations

r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi. The curve is y = sin x

The Attempt at a Solution

Do i let x(t)=t...?

No.

$\vec{r}(t)=x(t)\hat{i}+y(t)\hat{j}\,,$ so from what you are given, we see that x(t) =   ?   .