- #1

quietrain

- 655

- 2

## Homework Statement

find arc length of curve over the interval t(0,2pi)

r(t) = 10cos

^{3}t

**i**+ 10sin

^{3}t

**j**

## The Attempt at a Solution

i apply the formula integral ||r'(t)|| over the interval 0,2pi

i get integrate sqrt((-30cos

^{2}tsint)

^{2}+ (30sin

^{2}tcost)

^{2})

and then finally get 15sin

^{2}t |0 to 2pi

and i get 0

but the ans for the length is 60... :(

i believe it has got to do with me traversing the curve r(t) more than once when t goes from 0 to 2pi. but how do i know or show that that is the case? and how do i rectify this problem?

thanks!