No new ones.
If a curve C is described by the parametric equations x=f(t), y=g(t), , where and are continuous on and C is traversed exactly once as t increases from to , then the length of C is
If a curve C is described by the parametric equations x=f(t), y=g(t), , where and are continuous on , , then the surface area of the surface obtained by rotating C about the x-axis is given by S, where
This is just a change of variables problem!
Yes, that's right: this is just about change of variable. We start with our old formulas: for example, if f' is continuous on [a,b], then the length of the curve y=f(x), , is
Now, suppose that x and y are given parametrically, as x=f(t) and y=g(t). Then
where and . (Note: since must exist, x is travelling from left to right or from right to left, and doesn't stop; that is, ).