1.
瀹氱Н鍒嗙殑瀹氫箟
缁欏畾涓�涓湪鍖洪棿
[
a
锛?/p>
b
]
涓婄殑鍑芥暟
y
锛?/p>
f
(
x
)
锛?/p>
灏?/p>
[
a
锛?/p>
b
]
鍖洪棿鍒嗘垚
n
浠斤紝鍒嗙偣涓?/p>
a
锛?/p>
x
0
<
x
1
<
x
2
<
鈥?/p>
<
x
n
锛?/p>
1
<
x
n
锛?/p>
b
.
绗?/p>
i
涓皬鍖洪棿涓?/p>
[
x
i
锛?/p>
1
锛?/p>
x
i
]
锛岃鍏堕暱搴︿负
螖
x
i
锛屽湪杩欎釜灏忓尯闂翠笂鍙栦竴鐐?/p>
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i
锛屼娇
f
(
尉
i
)
鍦?/p>
[
x
i
锛?/p>
1
锛?/p>
x
i
]
涓婄殑
鍊兼渶澶?/p>
.
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S
锛?/p>
f
(
尉
1
)
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x
1
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f
(
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2
)
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x
2
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f
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锛嬧�︼紜
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(
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n
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.
鍦ㄨ繖涓皬鍖洪棿涓婂彇涓�鐐?/p>
味
i
锛屼娇
f
(
味
i
)
鍦?/p>
[
x
i
锛?/p>
1
锛?/p>
x
i
]
涓婄殑鍊兼渶灏忥紝璁?/p>
s
锛?/p>
f
(
味
1
)
螖
x
1
锛?/p>
f
(
味
2
)
螖
x
2
锛嬧�︼紜
f
(
味
i
)
螖
x
i
锛嬧�︼紜
f
(
味
n
)
螖
x
n
.
濡傛灉姣忔鍒嗗壊鍚庯紝鏈�澶х殑灏忓尯闂寸殑闀垮害瓒嬩簬
0
锛?/p>
S
涓?/p>
s
鐨勫樊涔熻秼浜?/p>
0
锛屾鏃?/p>
S
涓?/p>
s
鍚屾椂瓒嬩簬鏌?/p>
涓�涓浐瀹氱殑甯告暟
A
锛岀О
A
鏄嚱鏁?/p>
y
锛?/p>
f
(
x
)
鍦ㄥ尯闂?/p>
[
a
锛?/p>
b
]
涓婄殑瀹氱Н鍒?/p>
.
璁颁綔
蕛
b
a
f
(
x
)d
x
锛屽嵆
蕛
b
a
f
(
x
)d
x
锛?/p>
A
.
2.
瀹氱Н鍒嗙殑鎬ц川
鈶?/p>
蕛
b
a
1d
x
锛?/p>
b
锛?/p>
a
.
鈶?/p>
蕛
b
a
kf
(
x
)d
x
锛?/p>
k
蕛
b
a
f
(
x
)d
x
.
鈶?/p>
蕛
b
a
[
f
(
x
)卤
g
(
x
)]
d
x
锛?/p>
蕛
b
a
f
(
x
)d
x
卤
蕛
b
a
g
(
x
)d
x
.
鈶?/p>
蕛
b
a
f
(
x
)d
x
锛?/p>
蕛
c
a
f
(
x
)d
x
锛?/p>
蕛
b
c
f
(
x
)d
x
.
3.
寰Н鍒嗗熀鏈畾鐞?/p>
濡傛灉杩炵画鍑芥暟
f
(
x
)
鏄嚱鏁?/p>
F
(
x
)
鐨勫鍑芥暟锛屽嵆
f
(
x
)
锛?/p>
F
鈥?/p>
(
x
)
锛屽垯鏈?/p>
蕛
b
a
f
(
x
)d
x
锛?/p>
F
(
b
)
锛?/p>
F
(
a
).
銆愭�濊�冭鲸鏋愩�?/p>
鍒ゆ柇涓嬮潰缁撹鏄惁姝ｇ‘
(
璇峰湪鎷彿涓墦鈥溾垰鈥濇垨鈥溍椻�?/p>
)
(1)
璁惧嚱鏁?/p>
y
锛?/p>
f
(
x
)
鍦ㄥ尯闂?/p>
[
a
锛?/p>
b
]
涓婅繛缁紝鍒?/p>
蕛
b
a
f
(
x
)d
x
锛?/p>
蕛
b
a
f
(
t
)d
t
.(
鈭?/p>
)
(2)
鑻ュ嚱鏁?/p>
y
锛?/p>
f
(
x
)
鍦ㄥ尯闂?/p>
[
a
锛?/p>
b
]
涓婅繛缁笖鎭掓锛屽垯
蕛
b
a
f
(
x
)d
x
>0.(
鈭?/p>
)
(3)
鑻?/p>
蕛
b
a
f
(
x
)d
x
<0
锛岄偅涔堢敱
y
锛?/p>
f
(
x
)
锛?/p>
x
锛?/p>
a
锛?/p>
x
锛?/p>
b
浠ュ強
x
杞存墍鍥存垚鐨勫浘褰竴瀹氬湪
x
杞翠笅鏂?/p>
.(
脳
)