Calculus/Arc length/Solutions

1. Find the length of the curve from to .
:

Let

Then

:

Let

Then

2. Find the length of the curve from to .
:
:
3. Find the circumference of the circle given by the parametric equations , with .
:
:
4. Find the length of one arch of the cycloid given by the parametric equations , with .
:

Using the trigonometric identity

, we have

:

Using the trigonometric identity

, we have