Integration – Circle Area & Arc Length

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s