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Homework Help: Use of integration to find area

  1. Jan 22, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the area enclosed by the curve x = t^2 -2t, y = t^0.5 and the y axis

    2. Relevant equations
    Area of a parametric curve = ∫g(t) f'(t) dt, where g(t) = y and f(t) = x

    3. The attempt at a solution
    I believe that the limits of integration by be found by setting x and y equal to each other and solving for y. Do I still use the given equation, or do I have to modify it as this question asks about the y-axis, not the x-axis.

  2. jcsd
  3. Jan 22, 2015 #2


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    The limits of integration are the values of t where your curve intersects the y-axis. The y-axis is where the value of x equals 0. Solve that.
  4. Jan 22, 2015 #3
    I solved t^2 - 2t = x = 0 and I got t = 2 and t = 0, so those are my limits
    Now, do I still use ∫g(t) f'(t) dt or do I have to modify the equation to ∫f(t) g'(t) dt ?
  5. Jan 22, 2015 #4


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    You can actually use either one. One will give you the negative of the other. You can see this by looking at integration by parts.
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