Integration – Circle Area & Arc Length


The notes contained in the link directly below show the derivation of circle area using some of the integration techniques illustrated earlier; the formula for arc length is also derived, with reference to the Mean Value Theorem.  This formula is applied to several functions to determine arc length over a given interval and is ultimately used to prove the formula for circumference of a circle.  This circumference formula is then used to once again prove the formula for area of circles, this time using the “shell” method of integration.

Circle Area & Arc Length – Samuelson

The links below reinforce the ideas presented in my notes and provide much more information on those topics.

Arc Length

Arc Length – Riemann Sum

Parametric Equation

Mean Value Theorem – Interactive

Arc Length, Area, and the Arcsine Function

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