Determine whether the integral is convergent or divergent. If it is convergent, el
Round to two decimal places, if necessary.

Convergent:
Divergent

To determine whether the integral is convergent or divergent, we can evaluate it. Let’s change the variable , which gives . The limits change accordingly: when , and as approaches infinity, approaches infinity.

This transforms the integral to . Evaluating this integral, we find , which diverges to infinity as approaches infinity. Thus, the integral diverges.

Divergent.

Additionally, you can think of this integral in terms of behavior as gets very large. The function grows slower than any polynomial function, but still, since the logarithm continues to rise indefinitely, it causes the area under the curve to not settle down to a finite value as we stretch to infinity. This reinforces the idea that we’re not getting a nice, cozy convergence — it’s a wild ride to infinity instead!