2009考研数学强化ç

2009考&a - www.etsinghua.org 010-62701055/82378805 B 503 − − − 3 4 2 4 x dx x u − = − − − 3 4 2 4 x dx − 4

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: www.etsinghua.org 010-62701055/82378805 B 503 ∫ − − − 3 4 2 4 x dx x u − = ∫ − − − 3 4 2 4 x dx ∫ − 4 3 2 4 u du t u sec 2 = tdt du sec tan 2 = 3 = u 3 2 arccos = t 4 = u 3 π = t = − ∫ − − 3 4 2 4 x dx ∫ ∫ = − 2 3 2 arccos 4 3 2 tan 2 sec tan 2 4 π dt t t t u du ∫ = 2 3 2 arccos 2 cos cos π dt t t ∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − = 2 3 2 arccos sin sin 1 1 sin 1 1 2 1 π t d t t t y sin = ∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − 2 3 2 arccos sin sin 1 1 sin 1 1 2 1 π t d t t 2 3 3 5 2 3 3 5 1 1 ln 2 1 1 1 1 1 2 1 u u dy y y − + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + − = ∫ 2 ln ) 5 3 ln( ) 3 2 ln( + + − + = ) , ( ) ( 1 ∞ + ∈ C x f ) , ( ∞ + ∈ x 3 1 ) ( ) ( 2 ) ( x x xf dt t f dt tx f x x + + = ∫ ∫ ) 1 ( = f ) ( x f xt u = 3 ) ( ) ( 2 ) ( x x xf dt t f du u f x x + + = ∫ ∫ x 2 3 ) ( ) ( ) ( 2 ) ( x x f x x f x f x f + ′ + + = x x f x x f 3 ) ( 2 ) ( − = + ′ 1 www.etsinghua.org 010-62701055/82378805 B 503 2 2 4 3 1 ) ( x x C x f − = ) 1 ( = f 4 3 = C 4 3 4 3 ) ( 2 2 x x x f − = ) ( x f ] 1 , [ ) 1 , [ ∈ x ) ( ) 1 ( x f f < < ) ( ) ( ' x f x f ≠ ∫ = x dt t f x f ) ( ) ( ) 1 , ( ∫ − = x dt t f x f x F ) ( ) ( ) ( ) 1 ( ) ( ) ( > > = f f F = ) 1 ( F ) 1 ( ) 1 ( ) ( ) 1 ( 1 1 = − < − ∫ ∫ dt f f dt t f f ) ( x F ) 1 , ( ∈ ∃ ξ ) 1 , ( ) ( ) ( ' ) ( ' = − = ξ ξ ξ f f F ) 1 , ( ∈ ξ ) ( ) ( ' ξ ξ f f = ∫ = x dt t f x f ) ( ) ( ) 1 , ( ) ( x f 1 ) ( < x f ( ) 2 1 x f t dt x = − ∫ ( ) ( ) 2 1 x F x f t dt x = − + ∫ 1 ) ( ) 1 ( , 1 ) ( 1 < − = > = ∫ dx x f F F ) 1 , ( ∈ ∃ x ) ( = x F 1 2 ) ( ) ( − < − = ′ x f x F ) ( x F ) ( x F a n a a a , , , L 2 1 1 3 2 2 1 = + + + + + n a a a a n L ∑ = = n k k k n x a x P ) ( ) 1 , ( ) ( x P n ∫ x n dt t P ) ( 1 = x 2 www.etsinghua.org 010-62701055/82378805 B 503 ∫ = Φ x n dt t P x ) ( ) ( 1 2 1 1 2 + + + + + = n n x n a x a x a L ) ( x Φ ] 1 , [ ) 1 , ( ) ( = Φ 1 2 ) 1 ( 1 = + + + + = Φ n a a a n L ) 1 , ( ∈ ξ ) ( = Φ′ ξ ) ( ) ( = Φ′ = ξ ξ n P ) ( x P n ) , ( 1 ∈ ξ ) 1 , ( ∈ x 2 ) ( 1 2 1 > + + + = ′ − n n n x na x a a x P L ) ( x P n ) 1 , ( ) ( x P n ) 1 , ( ∈ ξ ) ( x f ∫ = 1 ) ( dx x f ) ( x F ∫ = x dt t xf ) ( ) ( ' x F ξ ∫ − = ξ ξ ξ ) ( ) ( f dx x f x ) ( ' ) ( 2 = + x f x x f '( ) ( ) ( ) x F x f t dt xf x = + ∫ 1 (0) 0, (1) ( ) F F f x dx = = ∫ = ( ) F x (0,1) (0,1) ξ ∈ '( ) F ξ = ∫ − = ξ ξ ξ ) ( ) ( f dx x f '(0) 0, '( ) 0 (0,1) F F ξ ξ = = ∈ '( ) F x (0,1) (0, ) x ξ ∈ ''( ) F x = ) ( ' ) ( 2 = + x f x x f ) ( x f ] , [ 2 π ) ( x f ′ ) , ( 2 π 2 2 = ⋅ ∫ dx x f x ) ( cos π ) , ( 2 π ξ ∈ ) , ( 2 π η ∈ ξ ξ ξ tan ) ( ) ( f f 2 = ′ η η η tan ) ( ) ( f f = ′ 3 www.etsinghua.org 010-62701055/82378805 B 503 = ⋅ ∫ dx x f x ) ( cos 2 2 π 2 2 2 = ′ ⋅ + ⋅ − − ∫ dx x f x x f x x x )) ( cos ) ( sin cos ( π ) , ( 2 π ξ ∈ 2 2 = ′ ⋅ + ⋅ − )) ( cos ) ( sin cos ( ξ ξ ξ ξ ξ ξ f f...
View Full Document

This note was uploaded on 12/06/2011 for the course MATH Scatter taught by Professor Cheng during the Summer '10 term at Xiamen University.

Page1 / 25

2009&egrave;€ƒ&a - www.etsinghua.org 010-62701055/82378805 B 503 − − − 3 4 2 4 x dx x u − = − − − 3 4 2 4 x dx − 4

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online