- #1

khemist

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- 0

## Homework Statement

Find an arc length parametrization of the curve r(t) = <e^t(cos t), -e^t(sin t)>, 0 =< t =< pi/2, which has the same orientation and has r(0) as a reference point.

## Homework Equations

s = int[0,t] (||r'(t)||)

## The Attempt at a Solution

So I found the derivative of r(t), and then normalized it. The problem is that I am left with a value that is negative under a radical, or a function that I simply do not have any idea how to integrate.

P.S: Sorry, I have no idea how to use that type of script which makes viewing functions more convenient...

My r'(t) = <(e^t(cos t - sin t)), (-e^t (cos t + sin t))>

I then normalized the derivative, where I got one of two functions:

e^t * (sqrt(-4sin t cost t) or sqrt(-e^t) * 2sqrt(sin t cos t)

But how would one integrate that? using by parts? My teacher claims that there would be nothing extremely difficult to integrate, but this problem seems to be proving otherwise...

Ps: Sorry, I do not know how to use that script which makes viewing functions more convenient..