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Math Help - Area of parametric curve

  1. #1
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    Area of parametric curve

    Hi, I'm having trouble finding the area of this parametric curve.

    The area is enclosed by the curve x = t^2-2t, y = t^0.5 and the y-axis.

    Thanks.
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  2. #2
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    Quote Originally Posted by triggy View Post
    Hi, I'm having trouble finding the area of this parametric curve.

    The area is enclosed by the curve x = t^2-2t, y = t^0.5 and the y-axis.

    Thanks.
    sketch a graph ... note that the area will be an integral w/r to y.

    A = \int_c^d x(t) \cdot y'(t) dt

    y = \sqrt{t}

    dy = \frac{1}{2\sqrt{t}} \, dt

    x = 0 at t = 0 and t = 2 ...

    A = \int_0^2 (t^2 - 2t) \cdot \frac{1}{2\sqrt{t}} \, dt

    can you finish from here?
    Last edited by skeeter; March 22nd 2009 at 12:31 PM. Reason: edit limits
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  3. #3
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    Oh alright, I got up to that last line.

    I integrated and got an answer of (1/5)*[2^(5/4)]/5 - (2/3)*[2^(3/4)].

    It doesn't appear to be the correct answer. I was wondering about the bounds. Is the bounds supposed to be in terms of t: the integral of 0 to 2?
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  4. #4
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    Quote Originally Posted by triggy View Post
    Oh alright, I got up to that last line.

    I integrated and got an answer of (1/5)*[2^(5/4)]/5 - (2/3)*[2^(3/4)].

    It doesn't appear to be the correct answer. I was wondering about the bounds. Is the bounds supposed to be in terms of t: the integral of 0 to 2?
    you're right, it should be 0 to 2 ... my mistake.
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