Three Methods to Find the Area of an Ellipse (and One Method that Doesn't Work)

In this video we discuss three methods to find the area of an ellipse (and then discuss one that doesn't work). The first is quite cute and very simple, using linear transformations on the unit circle; the second does the double integral with cartesian coordinates; and the third does the double integral with polar coordinates. Finally we discuss a parameterisation of the ellipse (x=a cos t, y = b sin t) where students often erroneously assume that they can integrate over 'r' and 't' in polar coordinates - spoiler alert, you cannot because 't' is not the CENTRAL angle.
[Note: There is yet another method to find the area of an ellipse, this time using Green's Theorem - see our video • Three Typical Question... ]
For more videos on conic sections see our playlist 'Conic Sections' at • Conic Sections
For more videos on double integrals see our playlist 'Double Integrals' at • Double Integrals
For more videos on polar functions see our playlist 'Polar Coordinates' at • Polar Coordinates
For more videos on undergraduate maths see our playlist 'Undergraduate Maths' at • Undergraduate Maths

[@grestyacademy]

For more videos on ellipses check out the Gresty Academy playlist 'Conic Sections' at th-cam.com/play/PLlX3COjsHPVBxwvdy15QINEwt2luDgoXJ.html

[@aliciaaquino7909]

this is great

[@grestyacademy]

Glad you think so!😎