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.
Find AREA.........
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
Cartesian equation:
(x2 + y2)2 = a2(x2 - y2)
圖片參考：http://www-history.mcs.st-andrews.ac.uk/Curvepics/Lemniscate/Lemniscate1.gif
回答 (1)
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
收錄日期: 2021-04-22 00:33:26
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