Chapter 11, Problem 64RE

Rejected quarters The probability that a random quarter is not rejected by a vending machine is given by the integral 11.4 ${\displaystyle {\int }_0^{0.14}{e}^{-102x^2}}$dx (assuming the weights of quarters are normally distributed with a mean of 5.670 g and a standard deviation of 0.07 g). Estimate the value of the integral by using the first two terms of the Maclaurin series for $e^{-102x^2}$.