Question

请问这段MATLAB代码有什么问题？ 积分后还是原式

syms t;syms a;a=5;int(exp(-0.4*(a*cos(t)+(25-a^2*(sin(t))^2)^0.5)),t,0,2*pi)

Answer 1

syms t;
syms a;
a=5;
int(exp(-0.4*(a*cos(t)+(25-a^2*(sin(t)).^2).^0.5)),t,0,2*pi)
Warning: Explicit integral could not be found.
找不到显式积分的解，所以建议用数值积分quad求解
syms t;
syms a;
a=5;
y=quad(@(t)exp(-0.4*(a*cos(t)+(25-a.^2*(sin(t)).^2).^0.5)),0,2*pi)

y =

3.6784

追问

大神帮忙看看，这个代码还有什么问题？
r=5;
a=0.4;
x=-5:0.1:5;
y=-5:0.1:5;
[X,Y]=meshgrid(x,y);
syms t;
Z=quad(@(t)exp(-(sqrt(X.^2+Y.^2)*cos(t)+(r^2-(X.^2+Y.^2)*(sin(t))^2).^0.5)*a),0,2*pi);

surf(X,Y,Z)
shading flat

追答

r=5;
a=0.4;
x=-5:0.1:5;
y=-5:0.1:5;
[X,Y]=meshgrid(x,y);
syms t;
for i=1:length(X)
for j=1:length(Y)
Z(i,j)=quad(@(t)exp(-(sqrt(X(i,j).^2+Y(i,j).^2).*cos(t)+(r^2-(X(i,j).^2+Y(i,j).^2).*(sin(t)).^2).^0.5)*a),0,2*pi);

end
end
Z1=real(Z);
surf(X,Y,Z1)
shading flat

你这个得用循环实现每个点积分的计算，否则矩阵维度不相等