Final answer:
To determine the values of p for which the integral converges, we use the Comparison Test. If we can find a function g(x) that is greater than or equal to f(x) and converges, then f(x) also converges. In this case, the integral converges for p > -1.
Step-by-step explanation:
To determine the values of p for which the integral converges, we need to consider the convergence criteria for integrals. One common criterion is the Comparison Test. If we can find another function g(x) such that g(x) ≥ f(x) for all x and the integral of g(x) converges, then the integral of f(x) also converges. So, we can compare the given integral to a known convergent integral and find the values of p for which it converges.
For example, let's assume the given integral is ∫(0 to ∞) x^p dx. We can compare it to the convergent integral ∫(0 to ∞) x^q dx, where q > -1. In order for the given integral to converge, p must be greater than -1. So, the values of p for which the integral converges are p > -1.