The Area of an Ellipse (and Circle)
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·r2.
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Trigonometric Substitution for Integrals: Example 2: Area of an Ellipse (and Circle)
Example: Find the area enclosed by the ellipse:
But we know that the ellipse is symmetrical with respect to both axes, thus the area is 4 times the area of the first quadrant:
Note: Although this is the equation of an ellipse, if we set a = b = r then we have also proven the famous equation of a circle:
