Use the Maclaurin expansion for e−t2 to express the function F(x) = ∫^x₀  e^−t2 dt as an alternating power series in x (Figure 3).

(a) How many terms of the Maclaurin series are needed to approximate the integral for x = 1 to within an error of at most 0.001?
(b) Carry out the computation and check your answer using a computer algebra system.

1 y = F(x) y = T15(x) 2 X