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## Homework Statement

Find the area Below ##y=0##,above ##y=lnx##, and to the right of ##x=0##

## Homework Equations

## The Attempt at a Solution

I thought an integral like ##\int_0^1 lnx \, dx##

then Its ##-∞## at ##x=0## So I used like ##lim(a→0)=\int_a^1 lnx \, dx## and from that it came

The integral result is ##xlnx-x## so ##1(ln1-1)-a(lna-1)## And if we take limit first term ##1(ln1-1)## is ##-1## but the other term bothers me.It will be ##0(-∞-1)##. I can think like ##lim (a→0)=a ln(a)## and that gave me ##0## but there's also ##+1## so the answer turns ##0## but its impossible.Where I am doing wrong ?