# Math Help - improper integrals

1. ## improper integrals

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?

2. You need to calculate $R=\int_1^\infty\left(\frac{1}{x}-\frac{1}{1+x}\right)dx=\ln2$

3. okay the first part is what I wrote out too, where does the ln2 take place in the question?

4. $R=\int_1^\infty\left(\frac{1}{x}-\frac{1}{1+x}\right)dx=\left[\ln x-\ln (1+x)\right]_1^\infty=\left[\ln{\frac{x}{1+x}}\right]_1^\infty$

The limit $\lim_{x \to \infty}\ln{\frac{x}{1+x}}=0$, so all we end up with is $-\ln\frac{1}{2}=\ln 2$