Re: [微積] 微積分的問題
※ 引述《ballballking (蛋蛋王)》之銘言：
: (1) ∫y^2/(9-y^2)^(5/2)dy
: (2) lim f(x)/[x(arctanx)] =? f(x)= ∫e^(-t)/(1+t^2)dt 從0積到x^2
: x→0
: (3) 求x^(2/3)+y^(2/3)=1 的周長
(1)let y=3cos(alpha),dy=-3sin(alpha)d(alpha)
原式
=S{[9cos^2(alpha)]/[9sin^2(alpha)]^(5/2)}[-3sin(alpha)] d(alpha)
=(-1) S [3^2cos^2(alpha)]/[3^4*sin^4(alpha)] d(alpha)
=(1/3^2) S cot^2(alpha)*[-csc^2(alpha)] d(alpha)
=(1/3^3) cot^3(alpha) + c
=(1/27)[y/sqrt(9-y^2)]^3 + c
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※ 編輯: wayne2011 (61.58.103.35), 07/23/2016 10:17:49
※ 編輯: wayne2011 (61.58.103.35), 07/23/2016 10:20:54
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