Determine whether the improper integral converges or diverges, and find the value of each that converges.
∫^[infinity]_1 1/x^1. dx

And with that we see that our integral diverges.

Step-by-step explanation:

For this case we assume the following integral:

Since 1.000 = 1 are equivalent. We can solve the integral and since we know that we got this:

And when we evaluate the limits using the fundamental theorem of calculus we got:

By properties we know that . But the is not defined since the natural log is a continuous increasing function so then:

And if we repplace this into our integral we got:

And with that we see that our integral diverges.

.

step-by-step explanation:

.