8.1 Challenging Integral Applications
Question #1 (Easy): Length of the Curve Using the Arc Length Formula
Arc length formula in Leibniz notation is: ∫ √ ( )
This requires taking the derivative of the given funwith respect to , then plugging into the
integral over the given interval]. Then solve using all integral techniques you have learned so far.
Using the arc length formula, find the length of the curve. Check your answer by noting that the curve is
part of a circle.
The arc length formula requires the derivative of y with respect to x, me. Since √
( ) . Thus: ( ) ( ) . Then, the arc of the length is
∫ √ ( √ ) ∫ √ ∫ √ ∫ √ ∫ √ . This we