matlab求常数A,B，C，使得∫（sin（x^2）-A-Bx-Cx^2)^2 最小。积分区间是（0，π/2） 数值分析题目：确定常数a,b,c的值，使得积分I=∫(0-x...
\u7528MATLAB\u6c42\u5e38\u6570A,B,\u4f7f\u5f97(x^2-A-Bx)\u57280\u2014\u20141\u4e0a\u7684\u79ef\u5206\u6700\u5c0f.\u4f7f\u7528matlab\u7684\u6781\u5c0f\u503c\u51fd\u6570fminsearch()\u5373\u53ef\uff0c\u53c2\u8003\u4ee3\u7801\u53ca\u7ed3\u679c\uff1a
>> f = @(a) quad(@(x)(sin(x.^2)-a(1)-a(2)*x-a(3)*x.^2).^2,0,pi/2);
>> fminsearch(f,[0,0,0])
ans =
-0.2139 1.3433 -0.3817
\u8868\u660eA=-0.2139\uff0cB= 1.3433\uff0cC= -0.3817\u65f6\u6ee1\u8db3\u8981\u6c42
\u9996\u5148\u5c06\u8be5\u79ef\u5206\u4ee4\u6210\u4e00\u4e2a\u4e09\u5143\u51fd\u6570g(a,b,c)\uff0c\u5373g(a,b,c)=\u222b(0-\u03c0) (sinx-a-bx-cx^2)^2dx\uff0c\u6c42\u8be5\u79ef\u5206\u7684\u6700\u5c0f\u503c\u5c31\u7b49\u4ef7\u6210\u6c42g(a,b,c)\u7684\u6781\u503c\u95ee\u9898\uff0c\u5229\u7528\u6781\u503c\u7684\u5fc5\u8981\u6761\u4ef6\uff0c\u5373g(a,b,c)\u5bf9a\u6c42\u504f\u5bfc=0\uff0cg(a,b,c)\u5bf9b\u6c42\u504f\u5bfc=0\uff0cg(a,b,c)\u5bf9c\u6c42\u504f\u5bfc=0\uff0c\u53ef\u5f97\u5230\u5173\u4e8ea,b,c\u7684\u65b9\u7a0b\u7ec4\uff0c\u89e3\u51fa\u8be5\u65b9\u7a0b\u7ec4\u5373\u4e3a\u6240\u6c42\u7ed3\u679c\u3002
使用matlab的极小值函数fminsearch()即可，参考代码及结果：>> f = @(a) quad(@(x)(sin(x.^2)-a(1)-a(2)*x-a(3)*x.^2).^2,0,pi/2);
>> fminsearch(f,[0,0,0])
ans =
-0.2139 1.3433 -0.3817
表明A=-0.2139，B= 1.3433，C= -0.3817时满足要求
绛旓細琛ㄦ槑A=-0.2139锛孊= 1.3433锛孋= -0.3817鏃舵弧瓒宠姹
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