Question

Consider the curve below.
x = (cos(t))^2
y = cos(t)
0 ≤ t ≤ 6π
(a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
(b) What is the length of the curve?

I have no idea on how to evaluate this integral. I know that for part b you just divide the answer of a by 6 and that would give me the arc length. Any help would be great!

Answer 1

Is it just me overthinking it?

Answer 2

nope. Look up arc length for parametric curves.

ds^2 = (dx/dt)^2 + (dy/dt)^2

The distance traveled is the arc length.