10.3 Parametric Arc Length

1
10.3 Parametric Arc Length Area of a Surface of
Revolution
2
OLD Arc Length
3
Arc Length if a curve C given by x f(t) , y
g(t), ? t ?, where f ? and g? are
continuous on ?, ? , and C is traversed exactly
once as t increases from ? to ?, then the length
of the curve is
4
Ex 1 Find the length of the curve.
5
OLD Surface Area
6
Surface Area if a curve C given by x f(t) , y
g(t), ? t ?, is rotated about the x-axis
where f ? and g? are continuous on ?, ? and
g(t)? 0, then the area of the surface is
7
Ex 2 Find the area of the surface obtained by
rotating the curve about the x-axis
8
Ex 3 Find the area of the surface obtained by
rotating the curve about the y-axis
9
10.3 pg. 6591, 3, 5, 9, 11, 21, 23, 25, 29