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

question 25

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

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