# Thread: area of parametric curve?

1. ## area of parametric curve?

I keep getting 0 for the area?

dy/dt = 36sin^2t
dx/dt = 36(1-cost)^2

integral from 0 -> 2pi of sqrt(36sin^2t + 36(1-cost)^2)

= integral 6sqrt(2) sqrt(1-cost) from 0-->2pi = 6sqrt(2) u^-1/2 = 0??

3. ## Re: area of parametric curve?

Originally Posted by lc99

I keep getting 0 for the area?

dy/dt = 36sin^2t
dx/dt = 36(1-cost)^2
Where are the 36's coming from? Also the derivatives don't have any squares in them.

integral from 0 -> 2pi of sqrt(36sin^2t + 36(1-cost)^2)

= integral 6sqrt(2) sqrt(1-cost) from 0-->2pi = 6sqrt(2) u^-1/2 = 0??
For rotation about the x axis you need a $2\pi y$ factor.

4. ## Re: area of parametric curve?

I have taken the limits from 0 to pi/2 according to your Question.

You can do this integral easily without calculator, but it will be a little long. I will give you the answer directly to shorten the time!