Integrals that cannot be evaluated in closed form sometimes can be evaluated approximately by using a series representation for the integrand. For example, the following integral is used for some probability calculations:

 

a. Obtain the Taylor series for e^-x2 about x = 0 and integrate the first six nonzero terms in the series to find I. Use the seventh term to estimate the error.

Compare your answer with that obtained with the MuPAD erf(t) function, defined as

I = Jo