Find AREA.........

👨🏻‍🏫 學術台數學

STEVIE-G™

2008-03-04 7:58 am

Find the area of Lemniscate of Bernoulli
Cartesian equation:
(x2 + y2)2 = a2(x2 - y2)

圖片參考：http://www-history.mcs.st-andrews.ac.uk/Curvepics/Lemniscate/Lemniscate1.gif

更新1:

Let the maximum x and minimum x be α and β.

回答 (1)

魏王將張遼

2008-03-04 8:23 am

✔ 最佳答案

Converting the Cartesian equation to polar equation:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Crazystevig1.jpg

Then, from θ = 0 to 2π, the first time that r becomes zero occurs at θ = π/4 and therefore the area can be found as:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Crazystevig2.jpg

參考: My Maths knowledge

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