How do you find the average value of

Heather Dickson

Heather Dickson

Answered question

2022-04-14

How do you find the average value of the positive y-coordinates of the ellipse x2a2+y2b2=1?

Answer & Explanation

coesarfaujs3t

coesarfaujs3t

Beginner2022-04-15Added 11 answers

This ellipse passes through (a, 0), (0, b), (-a, 0) and (0, -b)
The area of the ellipse is π ab
So the area of the upper half of the ellipse is πab2
The base of the upper half of the ellipse is of length 2a
So the average positive y value is πab22a=πb4

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