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Thread: Help with integration for Surface Area of Parametric Curve

  1. #1
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    Help with integration for Surface Area of Parametric Curve

    Help with integration for Surface Area of Parametric Curve-capture.png

    i got from the formula for surface area is

    2pi integral [(t-sint) * sqrt((1-cost)^2 - sin^2t)]

    I am having trouble integrating.

    I multiplied by the conjugate for sqrt(1-cost) after simplifying the inside. But then im very stuck.

    Please help!




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    Last edited by lc99; May 2nd 2018 at 09:40 PM.
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    Re: Help with integration for Surface Area of Parametric Curve

    I posted the wrong photo. It should be the one above
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  3. #3
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    Re: Help with integration for Surface Area of Parametric Curve

    The resulting integral is a mess. Are you sure you are expected to do it by hand?

    $\begin{align*}

    &S = 2\pi \displaystyle \int \limits_0^{\pi/2}~\sqrt{2-2\cos(t)}(t-\sin(t))~dt = \\ \\

    &\left . \dfrac{4}{3} \pi \sqrt{2-2 \cos (t)} \left(\cos (t)-3 t \cot \left(\dfrac{t}{2}\right)+5\right)\right|_0^{\pi/2} = \\ \\

    &\dfrac{2}{3} \sqrt{2} (10-3 \pi ) \pi

    \end{align*}$
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    Re: Help with integration for Surface Area of Parametric Curve

    how did you do it?

    im not sure. this question was on a review sheet.
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    Re: Help with integration for Surface Area of Parametric Curve

    Quote Originally Posted by lc99 View Post
    how did you do it?

    im not sure. this question was on a review sheet.
    i used software
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