Thread: Stuck on Another Direct Comparison Integral

I don't seem to be able to do these very well.

Use the Comparison Theorem to determine whether the integral is convergent or divergent:



I see two functions that might be of assistance:

so

But that won't help because is divergent, so it says nothing about a function that is less than it.


Then, I looked at the fact that on [0,1] so then . But is a proper integral, so it says nothing about an integral that is bigger than it.

AAAAAGH. I can't seem to get any of these figure out. What am I doing wrong?

Originally Posted by joatmon

I don't seem to be able to do these very well.

Use the Comparison Theorem to determine whether the integral is convergent or divergent:



I see two functions that might be of assistance:

so

But that won't help because is divergent, so it says nothing about a function that is less than it.


Then, I looked at the fact that on [0,1] so then . But is a proper integral, so it says nothing about an integral that is bigger than it.

AAAAAGH. I can't seem to get any of these figure out. What am I doing wrong?

for we have

Therefore for :



Hence the integral converges/diverges as converges/diverges

CB