Hello i have a question,
Find the area of region R that lies between y = 1/x and y = 1/(x+1) to the right of x = 1
I assume it has to do with bounding divergents can someone lend a hand?
$\displaystyle R=\int_1^\infty\left(\frac{1}{x}-\frac{1}{1+x}\right)dx=\left[\ln x-\ln (1+x)\right]_1^\infty=\left[\ln{\frac{x}{1+x}}\right]_1^\infty$
The limit $\displaystyle \lim_{x \to \infty}\ln{\frac{x}{1+x}}=0$, so all we end up with is $\displaystyle -\ln\frac{1}{2}=\ln 2$