the definite integral is: integral from 0 to 1 of ln(x). i used integration by parts (u=ln(x), du=1/x dx, dv=dx, v=x) to show that the integral is equal to:(adsbygoogle = window.adsbygoogle || []).push({});

[x*ln(x)] (1,0) - integral from 0 to 1 of dx.

this gives 1*ln(1)-0*ln(0)-(1-0)

ln(1)=0, so the equation is now

0*ln(0)-1

0*ln(0) is an indeterminate form, so i used the limit:

lim x-->0 x*ln(x)

lim x-->0 ln(x)/(1/x)

lim x-->0 (1/x)/(-1/x^2)

lim x-->0 -x

=0.

so the area is 0-1=-1, which doesn't make sense. what did i do wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definite integral help

**Physics Forums | Science Articles, Homework Help, Discussion**