8.1 Challenging Integral Applications
Arc Length: Overview
Finding the Length of an Arc
∑ | |
From the equation of any line segment: | √( ) ( ) √
From ( ) ( ) ( ). When the interval is divided into equal width o, then for any ith
subinterval: ( ) . Substituting back into the equation: | √ [ ( ) ]
√ [ ( ) ] As : ∑ | | ∫ √ [ ( )] by the definition.
Using Leibniz notation: ∫ √ ( ) .
For equations written as ( ), where