Statistical Inference — type-II error for a one-observation exponential test

If $x\ge1$ is the critical region for testing $H_0:\theta=2$ against alternative $H_1:\theta=1$, on the basis of single observation from the population $f(x,\theta)=\theta e^{-\theta x}$, where $0\le x<\infty$. The size of type-II error is