Finding Whether Improper Integrals Converge

[rocapp]

Hi all,

I'm having trouble with finding an improper integral.

The problem is ∫¹₀(xln(x))dx

My book says the answer is -1/4, but I do not understand how this is the case.

lim(xlnx) as x approaches 1^- = 0

lim(xlnx) as x approaches 0⁺ = ∞

So how does this value converge at -1/4?

Thanks in advance!

 

[pwsnafu]

lim(xlnx) as x approaches 0⁺ = ∞

What makes you say that? Did you try Lhopital?

 

[rocapp]

Ah. I see that. So now I just find the integral and from zero to one, correct?