The equations x = t + sin t, y = 1 – cos t, 0≤t≤2pi, define a curve C parametrically from the origin O to A(2pi, 0), which is rotated completely about Ox to form a surface S.
Find the length of the curve from O to A.
As I did so far,
dx/dt = 1 + cos t and dy/dt = sin t
Curve length OA =
My answer is 0. Where I did wrong?
But its correct answer is 8. Please help me.
Length is positive. So the length is the magnitude of the area enclosed by and the t-axis between t = 0 and t = 2 pi. How would you find that area ......? You'd draw a graph of versus t and break it up, right?:
since the signed area is negative from pi to 2pi ......
Capisce?