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Area of curve

  1. Jan 28, 2012 #1
    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. jcsd
  3. Jan 28, 2012 #2
    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.
  4. Jan 28, 2012 #3


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