The Area of an Ellipse (and Circle) (DTube)

in dtube •  21 days ago  (edited)


In this video I go over further into trigonometric substitution and this time do example 2 of the example series which so happens to be determining the area of an ellipse using integration. In the video I prove that the area of an ellipses is π·a·b where a and b are axes on the ellipses. Also since a circle is a type of an ellipse, with a = b = r then the area of a circle is also found to and is equal to the famous equation π·r^2.

Download the notes in my video: http://1drv.ms/1ENaae2

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/the-area-of-an-ellipse-and-circle

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Ellipses: Definition and Proof of Equation:

Trigonometric Substitution for Integrals: Example 1:

Trigonometric Substitution for Integrals:

Simple Proof of the Pythagorean Theorem:

Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1:

Half Angle Trigonometry Identities:

Derivative of Trigonometry Functions: Derivative of tan(x):
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I don't always prove the area of an ellipse but when I do I usually prove the area of a circle as well ;)

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/the-area-of-an-ellipse-and-circle