Final answer:
To solve the given integral, we can evaluate the double integral in two steps: first integrating with respect to y from y=0 to y=π, and then integrating the resulting function with respect to x from x=0 to x=π. However, the resulting integral of the sine integral function cannot be evaluated analytically and would require numerical methods.
Step-by-step explanation:
To solve the given integral, we need to evaluate the double integral ∫₀π ∫ₓπ sin(y)/y dydx.
First, let's integrate with respect to y from y=0 to y=π. The integral of sin(y)/y with respect to y is a well-known special function called the sine integral, denoted as Si(y). Evaluating this integral, we get ∫ sin(y)/y dy = Si(y). So, our double integral becomes ∫₀π Si(x) dx.
Next, we integrate Si(x) with respect to x from x=0 to x=π. However, Si(x) does not have a simple closed-form expression, so the integral cannot be evaluated analytically. We would need to use numerical methods, such as numerical integration techniques, to approximate the value of the integral.