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積分的意義 Integration. 組員:鐘志翔、羅有呈、梁君熙. 主題. 引言 . 基本概念 積分的符號 . 用處 圖形的面積 多邊形的面積 積分的意義. 引言 . 基本概念. - PowerPoint PPT Presentation
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Integration
..
. t t t t t x F
t t 0
x t x=t2 x t 2t d(t2)=2tdt d(x2)=2xdx
y x y=x2 d(x2)=2xdx y=x2 x 2x y=f(x)dy=f(x)dx
. A dA A
A
s ds r
dA ds
1/2r
dA ds
Q Q dQ dP Q Q Q Q Q
Q P P P Q
y=f(x) A x x x+x A A x y y+y A x 0 A y=f(x) Leibniz
RA(R)(1)RR(RR)RRA(R)A(R)
(2)R1R2R1R2A(R1)A(R2)
(3)R()R1R2RR1R2A(R)A(R1)A(R2) (3)R1R2Rn A(R)==A(R1)A(R2)A(Rn)
xyf(x)(f(x)0)xaxb(ba)
nxa (ba)xa (ba) xa (ba)Rnk(k12n)yf(x)xa (ba)xa (ba)xf[a (ba) a (ba)]mkMkk
mk MkRLn Un LnA(R)Unnf[ab]LnUnlimLnlimUnA(R)RA(R)fIk[a (ba) a (ba)]mkMk
tk IkTn mkf(tk)Mk LnTnUn limLnlimUnA(R)limTnA(R)tkIk
2-4 Leibniz