- #1

NastyAccident

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## Homework Statement

x=cos^2(t)

y=cos(t)

(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?

## Homework Equations

Length of an Arc: integral of alpha to beta sqrt((dx/dt)^2+(dy/dt)^2)

## The Attempt at a Solution

See attached PDF for full attempt as soon as it clears...

Originally, I attempted to find a factor to easily cancel the square root out. However, with this particular problem I couldn't. So, I took out my bazooka and used Trig sub for sqrt(4u^2+1) & Integration by parts (for sec^3(s))

My answer ends up being 12(-20+ln(3)-ln(7))... Which is negative plus it is way too high for (a)...

I integrated from 0 to pi (the length of one arc, which is the answer to b) and times it by six (there are a total of six arches).

Any help is greatly appreciated and will be thanked, I've been staring at this for about 2 hours now and I still can't figure out what is off.

NastyAccident