How can I integrate a non analytic function?

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davood
davood on 13 Jan 2014
Hello,
i am trying to integrate:
(1/b)*exp(b(thata(x)-1))*y_f '(x)
and find it's value at x_star. where b and x_star are constant. but the problem is that i don't have the analytical forms of theta(x) and y_f(x). i only have the following four coupled differential equations containing four functions (y_s(x), theta(x), theta_s(x) & y_f(x)):
-2*x*thata'(x)= thata''(x)-q*gamma*(y_s(x))^.66*(theta(x))^n-ksi*(theta(x)-theta_s(x))
-x*theta_s'(x)=zeta*(y_s(x))^-.66*(theta(x)-theta_s(x))
2*x*y_s'(x)=gamma*(y_s(x))^.66*(theta(x))^n
-2*x*y_f '(x)=(1/L)*y_f ''(x)+gamma*(y_s(x))^.66*(theta(x))^n
How can I evaluate that integral?
thank you

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