# Determine the values of #p# for which the integral below is convergent?

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#\int_1^\infty1/x^pdx#

I managed to integrate it, to #\lim_(t\rarr\infty)[((t^(-p+1))/(-p+1))-((1^(-p+1))/(-p+1))]# but now I am stuck :(

I managed to integrate it, to

##### 1 Answer

The integral converges for

#### Explanation:

So, we'll take the integral:

Let's assume

In that case,

and we have convergence as the exponent

Let's assume

In this case,

and we have divergence as the exponent

However, the limit we're evaluating requires that

Thus, the integral only converges for