Shouldn't that formula contain a one-dimensional normal CDF, not a two-dimensional CDF? Remember, after you use the Fundamental Theorem of Calculus, you are left with a one-dimensional integral. I believe that the correct formula should be a product of a one-dimensional PDF and a one-dimensional CDF. The argument to the PDF should be x, and the argument to the CDF should be (v-px)/SQRT(1-p^2). In addition to completing the square, it is necessary to make a change of variables in the CDF integral.