Answer:
To find the values of p for which the integral converges, we need to consider the exponent p in the integral. For the integral ∫(1/x^p) dx from 1 to 0, we need to determine the values of p that make the integral converge.
The integral ∫(1/x^p) dx converges when p > 1, as the function 1/x^p approaches 0 as x approaches infinity.
To evaluate the integral for those values of p, we can use the property of integrals:
∫(1/x^p) dx = [(x^(1-p))/(1-p)] + C
Substituting the limits of integration, we have:
∫(1/x^p) dx from 1 to 0 = [(0^(1-p))/(1-p)] - [(1^(1-p))/(1-p)]
Simplifying further, we get:
∫(1/x^p) dx from 1 to 0 = -1/(1-p) - 1/(1-p)
= -2/(1-p)
Therefore, the integral evaluates to -2/(1-p) for values of p > 1.