Is this integral improper? If yes - why?

Question

Is this integral improper? If yes - why? $$ \int\limits^2_0 \,\frac{1}{x-1} dx $$

Answer 1

Definition:

The integral $\int_a^b f(x)dx$ is called improper integral if:

• $a=+\infty$ or $b=\infty$ or both.

• $f(x)$ is unbounded at one or more points of $a\le x\le b$.

As @Git suggested verify which ones of above is satisfying the definition. You'll get the answer. ;-)

Answer 2

It is improper because the function "blows up" between the end points. That is, the function approaches $\pm \infty$ because the denominator is 0.

Answer 3

An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits.