Question

6. The function $E(x)$ below is important in probability and other sciences. $\qquad E(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt$ As we have discussed, there is no elementary antiderivative for the integrand, so values of this integral function are found using estimation techniques. (a) Use Simpson's Rule with $n = 16$ to estimate $E(1)$. (b) On $[0, 1]$, it can be shown that $\qquad \left| \frac{d^4}{dt^4} (e^{-t^2}) \right| \le 12.$ Use this to find an upper bound for the magnitude of the error from part (a). (c) Determine how large would $n$ need to be to obtain an estimate that is accurate to within $10^{-8}$.

          6. The function $E(x)$ below is important in probability and other sciences.
$\qquad E(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt$
As we have discussed, there is no elementary antiderivative for the integrand,
so values of this integral function are found using estimation techniques.
(a) Use Simpson's Rule with $n = 16$ to estimate $E(1)$.
(b) On $[0, 1]$, it can be shown that
$\qquad \left| \frac{d^4}{dt^4} (e^{-t^2}) \right| \le 12.$
Use this to find an upper bound for the magnitude of the error from part
(a).
(c) Determine how large would $n$ need to be to obtain an estimate that is
accurate to within $10^{-8}$.

6. The function E(x) below is important in probability and other sciences.
E(x) = (2)/(√(π))∫0^x e^-t^2 dt
As we have discussed, there is no elementary antiderivative for the integrand,
so values of this integral function are found using estimation techniques.
(a) Use Simpson's Rule with n = 16 to estimate E(1).
(b) On [0, 1], it can be shown that
| (d^4)/(dt^4) (e^-t^2) | ≤ 12.
Use this to find an upper bound for the magnitude of the error from part
(a).
(c) Determine how large would n need to be to obtain an estimate that is
accurate to within 10^-8.

Added by Carlos R.

Question

Please give Ace some feedback