1. The problem is to evaluate the improper integral $$\int_a^{+\infty} f(x) \, dx$$ which is defined as the limit $$\lim_{b \to \infty} \int_a^b f(x) \, dx$$. 2. The formula used is: $$\int_a^{+\infty} f(x) \, dx = \lim_{b \to \infty} \int_a^b f(x) \, dx$$ 3. To solve this, first compute the definite integral $$\int_a^b f(x) \, dx$$ treating $$b$$ as a finite upper limit. 4. Then take the limit as $$b$$ approaches infinity: $$\lim_{b \to \infty} \int_a^b f(x) \, dx$$. 5. If this limit exists and is finite, the improper integral converges to that value; otherwise, it diverges. 6. Without a specific function $$f(x)$$, this is the general approach to evaluate such improper integrals.