Calculate $E(X^2)$ of random variable $X$ ~ $N(3,4)$

Question

I need to find $E(X^2)$ of random variable $X$ ~ $N(3,4)$.

I can use the simple way:

$E(X^2) = \int_{-\infty}^{\infty} x^2 \cdot f(x) dx$,

in this case $f(x) = normal \space distribution \space pdf = \frac{1}{\sqrt{2\pi\sigma^2}}e^\frac{-(x-u)^2}{2\sigma^2}$.

I just wonder whether there's a simpler way to do it?

thanks in advance.

Answer 1

Since X is with mean 3 and variance 4, $E(X^2)=4+3^2=13$.