
Method of Monte Carlo
Approximate $\displaystyle \int^{1.96}_0 \frac{1}{\sqrt{2 \pi}}e^{\frac{1}{2} t^2}dt$
So I know that it's the PDF of a N(0,1) Distribution.
According to my textbook $\displaystyle \int^b_a g(x) dx = (b  a)E(g(x))$
since E(g(x)) = 0, but it doesn't look right.
Any help would be appreciated.

Integrand is positive
If I read this correctly, your g(x) is the exponential(t^2) with constants. This is always positive, so E(g(x)) can't be zero.

Nevermind, I figured it out. Thanks for your help though.