Re: [微積] 微積分的問題

[Honor1984 (希望願望成真)]

※ 引述《ballballking (蛋蛋王)》之銘言：
: (3)  求x^(2/3)+y^(2/3)=1 的周長

y = [1 - x^(2/3)]^(3/2)

y' = (3/2)√[1 - x^(2/3)](-2/3)x^(-1/3)

√[1 + y'^2] = √[1 + (1 - x^(2/3))/x^(2/3)]

             = x^(-1/3)
       1
S = 4 ∫ x^(-1/3) dx
       0

  = 4 (3/2) = 6

如果只允許x^(2/3)裡的x為正

(3/2)就不要乘以4

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