integral (numerical integration) base on r

dear all

i want to use integral (numerical integration) base on r

for W for the code below :

clc
clear all
m=9;
a=1;
u=[3.8317   7.0156  10.1735  13.3237  16.4706  19.6159  22.7601    25.9037   29.0468 ];
syms r
YY1 = zeros(1,m,'sym');
for j=1:m
    yy1 = zeros(1,100,'sym');
    yy0 = zeros(1,100,'sym');
    for i=1:100
        yy0(i)=(((-1)^(i-1))*((((u(j))/a)*r)^(2*(i-1))))/((2^(2*(i-1)))*((factorial(i-1))^2)) ;
        yy1(i)=(((-1)^(i-1))/((factorial(i-1))*(factorial(i))))*(((u(j))*r)/2)^(2*(i-1)+1) ;
    end
    YY1(j)=sum(yy1);
    YY0(j)=sum(yy0);
    W(j)=((YY1(j)/r)*YY0(j));
end

as it is obvious i have m=9 W that is base on r for diffrent u

i want to use numerical integration base on r in interval of 0 to 1

as i read matlab help for useing integral i should make function but i dont know to make function

i really appreciate if u could help me

Answer 1

[Walter Roberson]

a = 1;
u = [3.8317   7.0156  10.1735  13.3237  16.4706  19.6159  22.7601    25.9037   29.0468 ];
m = length(u);
i = (1 : 100) .';
u = reshape(u, 1, 1, []);
Wfun = @(r) sum((((-1).^(i-1))./((factorial(i-1)).*(factorial(i)))).*(((u).*r)/2).^(2*(i-1)+1)) ./r .* ...
    sum((((-1).^(i-1)).*((((u)/a).*r).^(2*(i-1))))./((2.^(2*(i-1))).*((factorial(i-1)).^2))) ;

W = squeeze( integral(Wfun, 0, 1, 'arrayvalued', true));

The output will be a vector the same length as u is.