Question

Can we solve this?
1
∫ (x ln x )dx
0

Answer 1

\[\int\limits_{1}^{0} x lnx dx\]

Answer 2

parts is my guess

Answer 3

improper integral, so it may not exist, but you can find the anti derivative by parts and then check

Answer 4

ooh that was wrong sorry

Answer 5

we can solve it

Answer 6

\[\int udv = uv-\int vdu\] with \(u=\ln(x), du =\frac{dx}{x}, dv = x, v = \frac{x^2}{2}\) should do it

Answer 7

"anti derivative" will be
\[\frac{x^2}{2}\ln(x)-\frac{x^2}{4}\] i think

Answer 8

now you are going to need to find that \(\lim_{x\to 0}\frac{x^2}{2}\ln(x)=0\)

Answer 9

I know that we can solve it by parts, but due to it's definite integral 0 and 1, so i think ln(0) is not possible.

Answer 10

when i tried this in wolfrom mathematica, it was giving answer of -1/4.

Answer 11

like satellite73 said, that's the answer... what you have to do is, find the limit \[\lim_{x \rightarrow 0} \frac{ x^{2} }{ 2 } \ln x\]... I think that's done if you know logarithmic series...

Answer 12

and you use L'Hopital's rule then.. try plugging in the logarithmic infinte series for log x...hope this hint helps..

Answer 13

thanks

Answer 14

welcome :)

Answer 15

hey, can u say, how to apply L'Hospital's Rule in finding Log[0]?