Here is a problem:

If you integrate that, you would get:

Now using the Fundamental theorem of calculus, F(b) - F(a) you would get an answer of 4ln(4) - 8.

But how is that answer even possible? If you used the formula F(b) - F(a), it would look something like this,

Wouldn't the log(0) give an indeterminate answer? Doesn't that automatically qualify the problem to be divergent?

Same thing with this problem:

Integrate that and you would get:

Use the fundamental theorem of calculus and you would get this:

2(sqrt4)ln(4)-4sqrt4-[(2sqrt0)ln(0)-4sqrt0]

This problem turns out to be divergent. But I'm not so sure if it is because of the ln(0) or what.

Please clarify how the answers are how they are for both of my questions. Thank you so much in advance.