# Area of curve

1. Jan 28, 2012

### bugatti79

1. The problem statement, all variables and given/known data

Find area of curve using area formula of Greens theorem

2. Relevant equations

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

3. The attempt at a solution

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

2. Jan 28, 2012

### 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.

3. Jan 28, 2012

### SammyS

Staff Emeritus
No.

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