It seems like you're working with mathematical expressions involving integrals and possibly functions like sine. Let's break down and clarify the problem step-by-step.

1. Integral Definitions:

   • $y_1(x) = \int_0^x \frac{\sin t}{t} \, dt$
   • $y_2(x) = \int_{\pi}^x \frac{\sin t}{t} \, dt$

   These are integral expressions for two functions, $y_1(x)$ and $y_2(x)$, involving the sine function divided by $t$.

2. Other Details:

   • The expression $0 \sin x = 0$ likely indicates an initial condition or a simplification since multiplying anything by 0 results in 0.

Understanding the Problem:

• $y_1(x)$ is an integral from 0 to $x$ of $\frac{\sin t}{t}$, which resembles the sine integral function $\text{Si}(x)$, though with a potential issue at $t = 0$ due to division by 0.

• $y_2(x)$ is another integral, but this one starts from $\pi$ and goes to $x$. It’s also in terms of $\frac{\sin t}{t}$.

Would you like to:

1. Solve these integrals?
2. Explore numerical approximations for specific values of $x$?
3. Analyze the behavior of $y_1(x)$ and $y_2(x)$ for small and large values of $x$?

Feel free to clarify or ask for further details!

Five Related Questions:

1. What is the significance of $y_1(x)$ and $y_2(x)$ in your problem?
2. Are you interested in exploring properties of the sine integral function $\text{Si}(x)$?
3. Would you like to explore the limits of these integrals as $x \to 0$ or $x \to \infty$?
4. Do you want to see the graphical behavior of $y_1(x)$ and $y_2(x)$?
5. Are there any conditions or boundary values you'd like to apply?

Tip:

Be cautious when dealing with integrals that have a singularity at $t = 0$, like $\frac{\sin t}{t}$, as they may require special handling or interpretation (such as defining it via a limit).