# Thread: Help with integration for Surface Area of Parametric Curve

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

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.

2. ## Re: Help with integration for Surface Area of Parametric Curve

I posted the wrong photo. It should be the one above

3. ## 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*}

4. ## 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.

5. ## Re: Help with integration for Surface Area of Parametric Curve

Originally Posted by lc99
how did you do it?

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