Example 14 __
Find the length, to three decimal places, of the curve (x − 2)^2 = 4y^3 from y = 0 to
y = 1.
SOLUTION: Since x − 2 = 2y 3/2 and , Equation (2) above yields
.Example 15 __
The position (x, y) of a particle at time t is given parametrically by x = t^2 and
. Find the distance the particle travels between t = 1 and t = 2.
SOLUTION: We can use (4): ds^2 = dx^2 + dy^2 , where dx = 2t dt and dy = (t^2 − 1)
dt. Thus, .
BC ONLYExample 16 __
Find the length of the arc of y = ln sec x from .
SOLUTION: