I am trying to find the area between two curves for this problem.
$$y = \frac{1}{x}$$
$$y=\frac{1}{x^2}$$
$$x = 2$$
I have not learned how to solve infinite regions and was told to look for the area between $x= 2$ and $x=1$ because it is the finite region and they intersect at $x=1$. However I do not know why this area is considered finite. Can someone please explain why it is considered a finite region and how to identify them?
Generaly, if $f(x)\leq g(x)$ for all $x\in[a,b]$, then the area between $f$ and $g$ is $$ Area=\int_{a}^{b}(g(x)-f(x))dx $$
In our case $$ Area=\int_{1}^{2}\left(\frac{1}{x}-\frac{1}{x^2}\right)dx =\left[\ln(x)+\frac{1}{x}\right]_{1}^{2} =\ln 2-\frac{1}{2} $$