The Function $f(x)=e^{-x^{2} / 2}$ Is Part of the Normal Probability Density Function (Or Bell-Shaped

Multiple Choice

The function $f(x) =e^{-x^{2} / 2}$ is part of the normal probability density function (or bell-shaped curve) .Find the Maclaurin series for $\int e^{-x^{2} / 2} d x$ by first finding the Maclaurin series for $f(x)$ and then integrating it term by term.

A) $\sum_{i=0}^{\infty} \frac{(-1) ^{i} x^{2 i+1}}{(2 i+1) 2^{i}(i !) }+C$
B) $\sum_{i=0}^{\infty} \frac{(-1) ^{i} x^{2 i}}{(2 i) 2^{i}(i !) }+C$
C) $\sum_{i=0}^{\infty} \frac{(-1) ^{i} x^{2 i+1}}{(2 i+1) 2^{i}(2 i !) }+C$
D) $\sum_{i=0}^{\infty} \frac{(-1) ^{i} x^{2 i}}{(2 i) 2^{i}(2 i !) }+C$