difficult integral

[wessicataylor]

what is the value of the integral of (dx/(x-1)) from a=0 to b=1

 

[wessicataylor]

does this integral diverge or is there a way to solve it?

 

[burakaltr]

what is the value of the integral of (dx/(x-1)) from a=0 to b=1

It's not too difficult if you know that

u'/u = dln(u)/du

so

ln(abs(x-1))+c is your integral, do not forget the absolute sign so how will you evaluate when a=0 to b=1 ?

 

[wessicataylor]

then it becomes ln(0)-ln(1), which diverges, right?

 

[burakaltr]

then it becomes ln(0)-ln(1), which diverges, right?

At x=1

1/(1-x) is not defined --> closes to an asymptote which is vertical.


http://www.wolframalpha.com/input/?i=1/(1-x)

 

[burakaltr]

http://www.wolframalpha.com/input/?i=Integrate+1/(1-x)+,from+0+to+1