Chapter 15: Multiple Integrals - Section 15.6 - Moments and Centers of Mass - Exercises 15.6 - Page 908: 10

$$M_{y} =1$$

Since \begin{align*} M_{y}&=\int_{0}^{\infty} \int_{0}^{e-x^{2} / 2} x d y d x\\ &=\lim _{b \rightarrow \infty} \int_{0}^{b} x e^{-x^{2} / 2} d x\\ &=-\lim _{b \rightarrow \infty}\left[\frac{1}{e^{x^{2} / 2}}-1\right]_{0}^{b}\\ &=1 \end{align*}