¹ÌÀûºÐ-±³°úA(001~007)

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1 . x«.,,,.., ,.. 86.

2 0 F(x)=x«(=, 2, 3, ) F'(x)=f(x).. F(x) F'(x)=f(x) x x x x xfi 2x 5x 6xfi x«. f(x) f'(x). f(x). ( ) idefiite itegral. : f(x)dx f(x) f(x)dx. F(x) f(x), F'(x)=f(x), F(x) f(x), :` f(x)dx q2 2E. : f(x)dx f(x), f(x). Z2 2c f(x) f(x),. F(x), G(x), H(x). F(x)=x +x Δapple F'(x)=3x + G(x)=x +x+ Δapple G'(x)=3x + H(x)=x +x-3 Δapple H'(x)=3x + x +x, x +x+, x +x-3 f(x)=3x

3 C =G{x} =F{x} x F(x)f(x), G(x) f(x) F'(x)=f(x), G'(x)=f(x) {G(x)-F(x)}'=G'(x)-F'(x) {G(x)-F(x)}'=f(x)-f(x)=0 0 G(x)-F(x)=C (C), G(x)=F(x)+C f(x) F(x)+C., C.. F'(x)=f(x). : f(x)dx=f(x)+c (, C ) : dx : dx. d x= : dx=x+c dx d x =2x : 2x dx=x +C dx. : 3x dx : 5x dx 2 f(x). (, C ) : f(x)dx=3x+c : f(x)dx=3x +4x+C : f(x)dx=x -2x +C : f(x)dx=;4!;x +;3!;x +2x+C 88.

4 02 x«f(x)= x«± (=0,, 2, ) + F'(x)=f(x).. F(x) F'(x)=f(x) x ;2!;x ;3!;x ;4!;x x x x«± + x«. x, ;2!;x x, ;3!;x x. { x«± } ' =x«+ x«. x«` x =., =0 : x dx=: dx : x dx=x+c : x«dx= x«± +C (, C ) + : xdx= x ± +C=;2!;x +C + : x dx= x ± +C=;3!;x +C 2+. : x dx : x dx : xfl dx. 89

5 03,,.. f(x), g(x) F(x), G(x) F(x)=: f(x)dx, F'(x)=f(x) G(x)=: g(x)dx, G'(x)=g(x) =kf(x) '=kf'(x). k {kf(x)}'=kf'(x)=kf(x) kf(x)=: kf(x)dx, kf(x)=k: f(x)dx : kf(x)dx=k: f(x)dx =f(x)+g(x) '=f'(x)+g'(x) {F(x)+G(x)}'=F'(x)+G'(x)=f(x)+g(x) F(x)+G(x)=: { f(x)+g(x)} dx, F(x)+G(x)=: f(x)dx+: g(x)dx : { f(x)+g(x)}dx=: f(x)dx+: g(x)dx {F(x)-G(x)}'=F'(x)-G'(x)=f(x)-g(x) F(x)-G(x)=: { f(x)-g(x)}dx, F(x)-G(x)=: f(x)dx-: g(x)dx : { f(x)-g(x)}dx=: f(x)dx-: g(x)dx. f(x), g(x) : kf(x)dx=k: f(x)dx (, k),. : { f(x)+g(x)}dx=: f(x)dx+: g(x)dx : { f(x)-g(x)}dx=: f(x)dx-: g(x)dx 90.

6 : (5x -2x+)dx : (x+)(x-2)dx : (5x -2x+)dx=5: x dx-2: xdx+: dx : (5x -2x+)dx=5 {;3!;x +C }-2 {;2!;x +C }+(x+c ) : (5x -2x+)dx=;3%;x -x +x+(5c -2C +C ) C. 5C -2C +C C : (5x -2x+)dx=;3%;x `-x `+x+c : (x+)(x-2)dx=: (x -x-2)dx : (x+)(x-2)dx=: x dx-: xdx-: 2dx : (x+)(x-2)dx=;3!;x `-;2!;x `-2x+C 2 F'(x)=2x+3, F(0)=2 F(x). F'(x)=2x+3 F(x)=: (2x+3)dx=x +3x+C F(0)=2 C. F(0)=2 F(0)=0 +0+C=2, C=2 F(x)=x `+3x+2. : (6x +2x-3)dx : (x-)(2x+)dx 2 F(x). F'(x)=-3x +4x-2, F()=0. 9

7 2..,. ;3!;Sh ;3!;.. 92.

8 0 cm, 0.5 cm, 0.25 cm... a, b,. 2. S, T,. 2 3 a 72 b S 4.5 T 7.5 T-S cm, 0.0 cm,, T-S.. 93

9 . ;!;. S, S«, T«S«<S<T«, S«T«S...,. =x x x= S. [0, ] x - 0, ;!;, ;@;,,, ;N;(=) =x@, S - x 0, {;!;}2, {;@;}2,, { }2, {;N;}2 2 -., S«- S«=;!; 0+;!; {;!;}2 ++;!; { }2 =x@ S«= { +2 ++(-) } 2 x - (-)(2-) S«= 6 S«=;6!;{-;!;}{2-;!;} 94.

10 T«- T«=;!; {;!;}2 +;!; ++;!; { }2 =x@ T«=+;!; {;N;}2 T«= { +2 ++(-) + } (+)(2+) T«= x T«=;6!; {+;!;}{2+;!;} S S«<S<T«. lim S«S lim T«S=;3!;. lim S«= lim ;6!;{-;!;}{2-;!;}=;3!; lim T«= lim ;6!;{+;!;}{2+;!;}=;3!; =x lim S«lim T«, lim S«lim T«. =x x=0, x= x S,. [0, ] x. x.. S. =x# x

11 r h V. h x h r x:r=;h; :h x=;r;.., r 2r 3r (-)r,,,, ;H; (-) V«r 2r 3r (-)r V«=;H; p{ }2 +p{ }2 +p { }2 ++p[ ]2 pr h V«= { (-) } pr h (-)(2-) V«= 6 h r h r V«=;6!;pr h {-;!;}{2-;!;} V V= lim V«V= lim ;6!;pr h {-;!;}{2-;!;}=;3!;pr `h S, h, ;3!;Sh. 96.

12 02 f(x)=6-x x x=, x=3. 6 f{x}=6-x@.. [, 3] 4 x xº, x, x, x, x. 2. f(x ) (k=, 2, 3, 4) xºx x x x x k x 2. f(x ) (x -x )f(x ). =f(x) [a, b], f(x)æ0 =f{x}., =f(x) S x=a, x=b x S. a b x [a, b] x xº (=a), x, x,, x,, x«(=b), [x, x ] (k=, 2,, ) Dx Dx= b-a. 97

13 Dx f(x ) S«S«=f(x )Dx+f(x )Dx+ S«=+f(x )Dx++f(x«)Dx S«=;K+! f(x )Dx ûx xº x x k-xk x a = =f{x} f{xapple} x = b x S. S= lim S«= lim ;K+! f(x )Dx =f(x)[a, b], defiite itegral. :Ab f(x)dx [a, b] f(x) a b f(x)dx. lim S«= lim ;K+! f(x )Dx., =f(x) a b, :Ab``f(x)dx. a, b.. : f(x)dx :Ab f(x)dx. f(x)[a, b] :Ab f(x)dx= lim ;K+! f(x )Dx {, Dx= b-a, x =a+kdx} =f(x) [a, b] :Ab f(x)dx f(x) S f(x) a S =f{x} b x S S. 98.

14 :) (x -)dx. 0 [0, ] x xº, x, x,, x,, x«[x, x ] (k=, 2,, ) Dx x Dx= -0 =;!; k =x@-` x x =0+kDx=;K; f(x)=x - f(x )=x -={;K;}2 - f(x )Dx=[{;K;}2 -];!;={ k -};!; ;K+! ;!;=;! ;K+!=;!; = [a, b] f(x)<0 f(x )<0, Dx>0 :Ab f(x)dx = lim ;K+! f(x )Dx<0 :) (x -)dx= lim ;K+! f(x )Dx k :) (x -)dx= lim ;K+! { -};!; k :) (x -)dx= lim {;K+! -;K+! } :) (x -)dx= lim { ;K+! k -} (+)(2+) :) (x -)dx= lim [ -] 6 :) (x -)dx=;3!;-=-;3@; :)2 2xdx :_!(4-x )dx. 99

15 03.,,. :A/ f(t)dt x x. =f(t) [a, b] f(t)æ0, [a, b] x a x S(x) S(x)=:A/ f(t)dt S{x} =f{t} a x b t. x Dx S(x) DS DS =f{t} D E ABCD. F A ûs ABCD B C EBCF EF. a x x+h b x+ûx t, x x+h DS=f(x+h)Dx DS =f(x+h) Dx 0 h Dx Dx 0 h 0.. DS S'(x)= lim = lim f(x+h)=f(x) Dx 0 Dx h 0, S(x) f(x).. f(t) [a, b], a x b d :A/ f(t)dt=f(x) dx S(x)=:A/ f(t)dt S'(x)=f(x) d dx :@/ (t +3t+2)dt=x +3x+2 00.

16 S(a) a a 0. S'(x)=f(x) S(x) f(x). f(x) F(x) S(x)=F(x)+C (, C ). S(x) S(a)=0 x=a S(a)=F(a)+C=0 C=-F(a), S(x)=F(x)-F(a), :A/ f(t)dt=s(x)=f(x)-f(a). x=b :Ab f(t)dt=f(b)-f(a). t x. :Ab f(x)dx=f(b)-f(a), F(b)-F(a) [F(x)]bA. =f{x} F{b}-F{a} a b x. f(x) [a, b], f(x) F(x) :Ab f(x)dx=[f(x)]ba=f(b)-f(a). :Aa f(x)dx=0 :Ab f(x)dx=-:ba f(x)dx. 0

17 x :A/ f(t)dt=x -4x+4 f(x) a.. x f(x)=2x-4 x=a :Aa f(t)dt=0 0=a -4a+4 a=2 2 :_0#(3x -2x)dx.. 3x -2x x -x =3x@-2x :_0#(3x -2x)dx=[x -x ]0_# =0-(-27-9) = x x :A/ f(t)dt=x -2x-8 f(x)a. 2 :!3 dx :_3@(3x -4x)dx :_2!2x dx :!0 (4x +3x )dx 02.

18 04. f(x) F(x) : kf(x)dx=kf(x)+c (k) :Ab kf(x)dx=[kf(x)]ba=kf(b)-kf(a) :Ab kf(x)dx=k{f(b)-f(a)}=k[f(x)]ba :Ab kf(x)dx=k:ab f(x)dx. c :Ac f(x)dx=[f(x)]ca=f(c)-f(a) =f{x} :Cb f(x)dx=[f(x)]bc=f(b)-f(c) :Ac f(x)dx+:cb f(x)dx={f(c)-f(a)}+{f(b)-f(c)} c f{x}dx a b f{x}dx c a c b x :Ac f(x)dx+:cb f(x)dx=f(b)-f(a) :Ac f(x)dx+:cb f(x)dx=:ab f(x)dx.. f(x), g(x) [a, b] :Ab kf(x)dx=k:ab f(x)dx (, k) :Ab { f(x)+g(x)}dx=:ab f(x)dx+:ab g(x)dx a<c<b. :Ab { f(x)-g(x)}dx=:ab f(x)dx-:ab g(x)dx :Ab f(x)dx=:ac f(x)dx+:cb f(x)dx. 03

19 dx :)3 x- dx dx -(x-) }dx (6x +2)dx =[2x =[2x ={2-(-6)}+{2-(-4)}=24 f(x) = x- x f(x)=-(x-) f(x)=-x+ -x- (xæ) f(x)= x- =[ -x+ (x ) 3 x :)3 x- dx=:) (-x+)dx+:!3 (x-)dx :)3 x- dx=[-;2!;x +x])+[;2!;x -x]3! :)3 x- dx={-;2!;+}+[{;2(;-3}-{;2!;-}]=;2%;. :!3 (x +2x)dx :_2!(4x -3x +)dx-:_2!(4x +3x -2x)dx :_2! 2x- dx :_2! x +2x-3 dx 04.

20 ,,,,,,,,, : f(x)dx, :Ab f(x)dx, [F(x)]bA.. : 2x dx : (x +x +)dx : (x+4)(x+2)dx : x(x+)(x+2)dx 2 :)2 x(2-x)dx. 3. :_2@{-(x-3) }dx :)4 x(x-)dx :)4 3x(x-2)dx-:@4 3x(x-2)dx 4 :_2@ x+ dx :_2! x - dx 5 x m F(x) F(x)=kx (, k, N). F(x) x=a x=b, F W W=:Ab F(x)dx (, J). 0.2 m 0.3 m 20 N. 0.3 m 0.4 m.. 05

21 .. x m x /m.(x /m m x.) 0 m 0 /m. x`m` x` /m@ 50 m 20 m,. ( )_( ). x m (x+dx) m x`m` 50Dx m. ûx`m`` x /m 50xDx 0 m 20 m.,. :)2 0 50x dx=[25x ]2)0 =0000( ) 0`m 20`m 50`m` 20`m` 06.

-주의- 본 교재는 최 상위권을 위한 고난이도 모의고사로 임산부 및 노약자의 건강에 해로울 수 있습니다.

-주의- 본 교재는 최 상위권을 위한 고난이도 모의고사로 임산부 및 노약자의 건강에 해로울 수 있습니다. Intensive Math 극악 모의고사 - 인문계 등급 6점, 등급 점으로 난이도를 조절하여 상위권 학생들도 불필요한 문제에 대한 시간 낭비 없이 보다 많은 문제에서 배움을 얻을 수 있도록 구성하였습니다. 단순히 어렵기만 한 문제들의 나열이 아니라 수능에 필요한 대표 유형을 분류 하고 일반적인 수험환경에서 흔하게 배울 수 있는 내용들은 과감하게 삭제 수능시험장