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