b 1 f(x)x≈Sn=b∑A[f(x)+4f(x-1)+f(x+1) k k=0 复合 Simpson公式 复合抛物线公式 =b2(a)+2/(x1)+2/()+(b k+ k=0 k=1 l=4时,可得复合 Cotes求积公式 复合 Cotes公式 b 八(xkCn=b∑cf(x) k=0i=0 如∑[7f(xk)+32(x1)+12(x2)+32f(x3)+7(xk+1 k=0 4 4 I7f(a)+∑[32f(x1)+12f(x,2)+32f(x 901 ∑f(x)+7/(b) k=0 k k 3力+14复合Simpson公式 复合抛物线公式 n b a f x dx S ò ( ) » å - = + + = + + 1 0 1 2 1 [ ( ) 4 ( ) ( )] 6 1 n k k k k h f x f x f x [ ( ) 4 ( ) 2 ( ) ( )] 6 1 1 1 0 2 f a f x 1 f x f b n b a n k k n k k + + + - = å å - = - = + l = 4时,可得复合Cotes求积公式 åå - = = + = 1 0 4 0 4 (4) ( ) n k i i k i n h C f x b a f x dx » C ò ( ) [7 ( ) 32 ( ) 12 ( ) 32 ( ) 7 ( )] 90 1 1 0 4 3 4 2 4 1 + - = + + + = å + + + + k n k k k k k f x f x f x f x f x h [7 ( ) [32 ( ) 12 ( ) 32 ( )] 14 ( ) 7 ( )] 90 1 1 1 0 4 3 4 2 4 1 f a f x f x f x f x f b n b a n k k n k k k k + + + + + - = å å - = - = + + + 复合Cotes公式