14. The area of the closed figure formed by the parabola $y^{2}=a x(a>0)$ and the line $x=1$ is $\frac{4}{3}$, then the coefficient of the term containing $x^{-18}$ in the expansion of the binomial $\left(x+\frac{a}{x}\right)^{20}$ is $\qquad$ .
$2 \int_{0}^{1} \sqrt{a x} \mathrm{~d} x=\left.\frac{4}{3} \sqrt{a} x^{\frac{3}{2}}\right|_{0} ^{1}=\frac{4}{3} \sqrt{a}=\frac{4}{3} \Rightarrow a=1$, so $T_{r+1}=C_{20}^{r} x^{20-r}\left(\frac{1}{x}\right)^{r}=C_{20}^{r} x^{20-2 r}$. When $r=19$, the coefficient of the term containing $x^{-18}$ in the expansion is 20.