Why is the following function $\int_E\frac{y}{x} e^{-x}\sin x\;d\mu$ measurable?

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Why is the following function inside the integral $\int_E\frac{y}{x} e^{-x}\sin x\; d\mu$ measurable where $\mu$ is the product measure on $R$ with itself and $ E = \{ (x,y) : 0 \leq y \leq \sqrt{x}\}$?