【精选】1997考研数学四.pdf
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1997
f x
1 y f ln x e ( ) f dy _________________.
( )
f x ⎡1 ⎤
e ( ) f ′ ln x + f ′ x f ln x dx
⎢ ( ) ( ) ( )⎥
⎣x ⎦
f x f x f x
dy d ⎡f ln x e ( )⎤ ⎡df ln x ⎤⋅e ( ) + f ln x de ( )
⎣ ( ) ⎦ ⎣ ( )⎦ ( )
⎡1 ⎤ f x f x
f ′ ln x dx =⋅e ( ) +f ln x e ( ) ⋅f ′ x dx
⎢ ( ) ⎥ ( ) ( )
⎣x ⎦
f x ⎡1 ⎤
e ( ) f ′ ln x =+ f ′ x f ln x dx
⎢ ( ) ( ) ( )⎥
⎣x ⎦
1 3 1 1
2 f x =+x f x dx , f x dx _______________.
( ) 1+x 2 ∫0 ( ) ∫0 ( )
π
3
1
f x dx A,
∫0 ( )
1 1 dx 1 3
A f x dx +A x dx
∫0 ( ) ∫0 1+x 2 ∫0
1 Ax 4 1 π A
arctan x =+ =+
0 4 0 4 4
π
A .
3
⎡0 1 1 1 1⎤
⎢ ⎥
⎢1 0 1 1 1⎥
⎢1 1 0 1 1⎥
3 n A ⎢ ⎥, A ____________.
⎢ ⎥
⎢1 1 1 0
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