Chapter 7.8, Problem 72E

Estimate the numerical value of ${\displaystyle {\int }_0^{\infty }{e}^{-x^2}}dx$ by writing it as the sum of ${\displaystyle {\int }_0^4{e}^{-x^2}}dx$ and ${\displaystyle {\int }_4^{\infty }{e}^{-x^2}}dx$. Approximate the first integral by using Simpson’s Rule with n = 8 and show that the second integral is smaller than ${\displaystyle {\int }_4^{\infty }{e}^{-4x}}dx$ , which is less than 0.0000001.