Any idea how to come up with the integral from 0 to t , of e^((x^2)/2) ?

Question

You can't really find an anti derivative of the integrand , so have to apply some kind of fundamental theorem of calculus thing here.

Answer 1

You have to use a specialized function for this one:

√(π/2) Erfi(t/√2)

Check out the Wolfram site on the Erfi function. Compare this function with the Erf function. If the function had been

e^(-(x^2)/2)

instead, then the indefinite integral would have been of the Erf form.

Answer 2

This function must be integrated numerically and values tabulated so that it becomes a "look-up" solution.