calculus - Evaluate: $int_{gamma}textrm {x.n(x)} dstextrm{(x)}$

Let $\textrm{x}=(x,y)\in\mathbb{R^2}$. Let $\textrm{n(x)}$ denotes the unit outward normal to the ellipse $\gamma$ whose equation is given by

$$\frac{x^2}{4}+\frac{y^2}{9}=1$$ at point $\textrm{x}$ on it. Evaluate: $$\int_{\gamma}\textrm {x.n(x)} ds\textrm{(x)}.$$