1. The problem is to find the integral equation of a typical senior university exam level. 2. Integral equations usually relate a function to its integral, and a common form is the Fredholm integral equation of the second kind: $$f(x) = g(x) + \lambda \int_a^b K(x,t) f(t) \, dt$$ where: - $f(x)$ is the unknown function to be found. - $g(x)$ is a known function. - $K(x,t)$ is the kernel function. - $\lambda$ is a parameter. - The limits of integration are $a$ to $b$. 3. Another example is the Volterra integral equation of the second kind: $$f(x) = g(x) + \lambda \int_a^x K(x,t) f(t) \, dt$$ where the upper integral limit is variable. 4. To illustrate, let's state a specific integral equation problem: Find $f(x)$ satisfying $$f(x) = \sin x + \int_0^\pi \cos(x - t) f(t) \, dt$$ where $g(x) = \sin x$, $\lambda=1$, $K(x,t) = \cos(x-t)$, $a=0$, $b=\pi$. 5. This is a Fredholm integral equation of the second kind with given kernel and known function. 6. The solution methods typically involve eigenfunction expansions, successive approximations, or converting to differential equations in some cases. 7. The presented equation illustrates a typical senior university integral equation problem. Final answer: A senior university exam level integral equation is $$f(x) = g(x) + \lambda \int_a^b K(x,t) f(t) \, dt$$ or specifically, $$f(x) = \sin x + \int_0^\pi \cos(x - t) f(t) \, dt$$