Question

calc 3 help
suppose that the position function of a particle moving along a circle in the xy plane is r = 5cos(2pi)ti+5sin(2pi)tj. what is the distance traveled by the particle during the time interval t=0 to t=1

Answer 1

use the parametric arc length formula

Answer 2

\[ds=\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}dt\]\[L=\int_a^bds\]

Answer 3

Correct.

\[\int\limits_{0}^{1} \left| r'(t) \right|dt\]

Answer 4

oh. Didnt saw the "i" and "j". use @TuringTest 's formula instead

Answer 5

eh, same thing really

Answer 6

but it is easier

Answer 7

So I just find ds, and integrate it along 0 and 1?

Answer 8

yep