Let $$f\left(x\right)=K\left[sin^2\left(6x\right)+3cos^2\left(x\right)sin^2\left(4x\right)+1\right]e^{-\frac{x^2}{2}},\:-\infty <x<\infty $$
be the probability density function of a random variable X and K is the normalizing constant. I am trying to find a Monte Carlo estimate $\hat{K}$ of K by sampling from the standard normal but I'm having some trouble.
Since $f\left(x\right)$ is a density function,
$$K\:=\:\frac{1}{\int \:\:\left[sin^2\left(6x\right)+3cos^2\left(x\right)sin^2\left(4x\right)+1\right]e^{-\frac{x^2}{2}}\:dx}$$
Should I use K as $g\left(x\right)$ to compute the formula below?
