8.1 Arc Length Question #2 (Medium)
8.1 Challenging Integral Applications
Question #2 (Medium): Integral Representation of the Length of the Curve
When the function is given as in terms of , take the derivative of in terms of , thus
If the function is given as in terms of , no need to rearrange to have written in terms of . take the
derivative of it as it is, thus
, and taking the integral in terms of .
Set up an integral representing the length of the curve. Then evaluate the exact length of the curve.
First take the derivative of the given function. Thus,
. Plug into the formula for the
. Based on the identity
. multiply by
Therefore, the length of the curve over the interval