py0214
春芽
共回答了15个问题采纳率:86.7% 举报
1.4
Trapezoidal:
sum [(b-a)/N]*[f(x0)+2f(x1)+2f(x2)+...+2f(xN-1)+f(xN)]/2
Midpoint:
sum [(b-a)/N]*[f(x 1/2)+f(x 3/2)+...+f(x N-1/2)]
Simpson:
sum [(b-a)/N]*[f(x0)+4f(x 1/2)+2f(x1)+4f(x 3/2)+2f(x2)+...+4f(x N-1/2)+f(xN)]/6
2.此处N=4,a=0,b=1,所以
Trapezoidal=(1/4)*[f(0)+2f(1/4)+2f(1/2)+2f(3/4)+f(1)]/2
Midpoint=(1/4)*[f(1/8)+f(3/8)+f(5/8)+f(7/8)]
Simpson=(1/4)*[f(0)+4f(1/8)+2f(1/4)+4f(3/8)+2f(1/2)+4f(5/8)+2f(3/4)+4f(7/8)+f(1)]/6
然后带入值即可
(a)3.131176
(b)3.146801
(c)3.141593
3.此处N=4,a=1,b=3,所以
Trapezoidal=(2/4)*[f(1)+2f(3/2)+2f(2)+2f(5/2)+f(3)]/2
Midpoint=(2/4)*[f(5/4)+f(7/4)+f(9/4)+f(11/4)]
Simpson=(2/4)*[f(1)+4f(5/4)+2f(3/2)+4f(7/4)+2f(2)+4f(9/4)+2f(5/2)+4f(11/4)+f(3)]/6
然后带入值即可
(a)1.116667
(b)1.089755
(c)1.098725
1年前
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