Differentiation under the integral sign.

The value of a definite integration of f(x,α) is function of α (parameter), F(α) say. To find F'(α), first we have to evaluate the integration of f(x,α) and then differentiate F(α) w.r.t. α . However, it is not always possible to evaluate the integral and then to find its derivative. Such problems are solved by reversing the order of the integration and differentiation i.e, first differentiate F(x,α) partially w.r.t. ‘‘α’’ and then integrate it.