<p>Consider the function \[f(t) = \int_0^t e^{-x^2} \, dx.\]  This is an an important function in probability, but it can be hard to work with because it isn't possible to write down an antiderivative for \(e^{-x^2}\) using the &ldquo;elementary&rdquo; functions we have on hand.  So if we want to compute \(f(#{latex(desired_point)})\), we'll have to do some work.  Put together what you know about \(e^x\), about integrating power series, and about approximating alternating series to evaluate \(f(#{latex(desi