matlab中带参数的定积分求解

来个简单点的。

步长统一取0.01

代码如下：

>> clear

phi=[0:0.01:pi]';

r=sqrt(1.16-0.8*cos(phi));

beta=[-2:0.01:2]';

%计算矩阵K

for i=1:length(r)

for j=1:length(beta)

K(i,j)=sqrt(4*r(i)/((1+r(i))^2+beta(j)^2));

end

end

%计算被积函数，进而求出矩阵F(K)和E(K):

theta=0:0.01:pi/2;

for i=1:length(r)

for j=1:length(beta)

for k=1:length(theta)

f(i,j,k)=1./sqrt(1-K(i,j)^2*sin(theta(k)^2));

e(i,j,k)=sqrt(1-K(i,j)^2*sin(theta(k)^2));

end

end

end

%计算矩阵F(K)和E(K)，以及M的被积函数m

for i=1:length(r)

for j=1:length(beta)

F(i,j)=sum(f(i,j,[1:length(theta)]))*0.01;

E(i,j)=sum(e(i,j,[1:length(theta)]))*0.01;

m(i,j)=(1-0.4*cos(phi(i)))/(K(i,j)*sqrt(r(i)^3))*(1-K(i,j)^2/2)*(F(i,j)-E(i,j));

end

end

%计算向量M

for j=1:length(beta)

M(j)=sum(m([1:length(r),j]))*0.01;

end

%作图

plot(beta,M)

计算结果见上传的文档