Question

matlab 不定积分 费米积分

想对y=x^0.5/(1+exp(x-s))进行积分0到无穷大，s是个常数，s=0时候可以得到答案，s=2就不行了，积分结果其实已知在1到3之间，只是想知道个准确数值，但系统提示Warning: Explicit integral could not be found.程序如下：
>> syms x;s=0;
y=x^0.5/(1+exp(x-s));
Fn=int(y,x,0,inf)

Fn =

1/2*pi^(1/2)*zeta(3/2)-1/4*pi^(1/2)*zeta(3/2)*2^(1/2)

>> 1/2*pi^(1/2)*zeta(3/2)-1/4*pi^(1/2)*zeta(3/2)*2^(1/2)

ans =

0.6781

>> syms x;s=2;
y=x^0.5/(1+exp(x-s));
Fn=int(y,x,0,inf)
Warning: Explicit integral could not be found.
> In E:\profile\matlab\toolbox\symbolic\@sym\int.m at line 58

Fn =

int(x^(1/2)/(1+exp(x-2)),x = 0 .. inf)

如果用quad怎么做？
>> s=0;
f=inline('y=x^0.5/(1+exp(x-s))','x');quad(f,0,10);
??? Error using ==> inlineeval
Error in inline expression ==> y=x^0.5/(1+exp(x-s))
??? Error: Assignment statements do not produce results. (Use == to test
for equality.)

Error in ==> E:\profile\matlab\toolbox\matlab\funfun\@inline\feval.m
On line 34 ==> INLINE_OUT_ = inlineeval(INLINE_INPUTS_, INLINE_OBJ_.inputExpr, INLINE_OBJ_.expr);

Error in ==> E:\profile\matlab\toolbox\matlab\funfun\quad.m
On line 59 ==> y = feval(f, x, varargin{:});
我本来想用quad这样做，因为我还想计算当积分结果Fn为某值时，s=？可是不行。如果想求s要怎么做呢？

Answer 1

这样如何？

clc;clear;
myfun0=inline('x.^0.5./(1+exp(x-0))','x');
myfun1=inline('x.^0.5./(1+exp(x-1))','x');
myfun2=inline('x.^0.5./(1+exp(x-2))','x');
Q0 = quadl(myfun0,0,100)
Q1 = quadl(myfun1,0,100)
Q2 = quadl(myfun2,0,100)

结果：
Q0 =

0.6781

Q1 =

1.3964

Q2 =

2.5025