I need to solve this integral with a Taylor Series. I'm uncertain how to proceed because when I approximate the series, it seems to diverge (I don't believe the integral diverges). I'm supposed to use the Taylor Series of arcsos(2x^2), and then integrate.

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?