Taylor expansions and integration.

[JamesHG]

I have a short doubt: Let f(x) be a fuction that can't be integrated in an analytical way . Is anything wrong if I expand it in a Taylor' series around a point and use this expansion to get the value of the definite integral of the function around that point? Suppose that the interval between the integral limits it's short so that the expansion is a good approximation to the function in that interval.
Thanks!

 

[eys_physics]

I have a short doubt: Let f(x) be a fuction that can't be integrated in an analytical way . Is anything wrong if I expand it in a Taylor' series around a point and use this expansion to get the value of the definite integral of the function around that point? Suppose that the interval between the integral limits it's short so that the expansion is a good approximation to the function in that interval.
Thanks!

If the function is analytic around the point (i.e. all the derivatives exist and or finite at the point), I cannot see any problem. Obviously, unless you use infinite number terms it will usually only be an approximation to your integral over f(x).