※ 引述《kelvin811 (sheila)》之銘言：
: find a formula for the area of a disk of radius r
: Hints: the function f(x)=√(r平方-x平方) on 〔0,r〕
: describes a quarter circle of radius r, substitute
: u= sin^-1 (x/r)
: ps.拜託善心的鄉民們~不是敝人平時不看書，而是已經離開書本四五年>"<
quarter circle:
int[0,r][f(x),dx] = int[0,r][sqrt(r^2-x^2),dx]
= r*int[0,r][sqrt(1-sin^2(u)),dx] ... as sin(u) = x/r
= (r^2)*int[0,pi/4][cos^2(u),du] ... as dx=r*cos(u)du
= pi(r^2)/4
circle area = 4*quarter = pi(r^2) ... ans
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※ 編輯: Rasin 來自: 114.38.196.30 (02/18 16:08)