Matlab gives no result when I use the integral function - matlab

Question

When trying to calculate the Integral of two variables, I got nothing!
Here is the code:
syms x;
a=0.4;
theta=(9 - 4*x*(5*x - 141/25))^(1/2)/2 - 3/2;
theta_prime=-(40*x - 564/25)/(4*(9 - 4*x*(5*x - 141/25))^(1/2));
g=(1/theta)*theta_prime
s=(1+a*(theta-1))*(g)^2
sgen = int(s,x,0.1,1) %x=0.1:0.1: 1
What was my mistake?
It supposed to be one value, such as '4.86'.
Please advise.

Answer 1

sgen is a symbolic object representing the integral of your function s. You can cast it to double to obtain a numerical value for your integral:
syms x;
a=0.4;
theta=(9 - 4*x*(5*x - 141/25))^(1/2)/2 - 3/2;
theta_prime=-(40*x - 564/25)/(4*(9 - 4*x*(5*x - 141/25))^(1/2));
g=(1/theta)*theta_prime;
s=(1+a*(theta-1))*(g)^2;
sgen = double(int(s,x,0.1,1)) % returns 4.8694
But if you're not interested in the symbolic equation for the integral, there really is no point in using the symbolic toolbox for this. It is much faster to compute the integral numerically. One way to do so is to create a function s(x) and then use integral to find the numerical integration. Do note that s(x) must be vectorized on the x variable for this to work (integral will call it with a vector of x values to save time). For vectorized computation, it is necessary to add dots in front of some of the *, / and ^ operators. This is the result:
a = 0.4;
theta = #(x) (9 - 4*x.*(5*x - 141/25)).^(1/2)/2 - 3/2;
theta_prime = #(x) -(40*x - 564/25)./(4*(9 - 4*x.*(5*x - 141/25)).^(1/2));
g = #(x) (1./theta(x)).*theta_prime(x);
s = #(x) (1+a*(theta(x)-1)).*g(x).^2;
sgen = integral(s,0.1,1.0) % returns 4.8694