Answer
The integral diverges.
Work Step by Step
The integral is $\displaystyle\int_0^2\frac{7}{2-x}dx$. However, as the integrand approaches $x=2$, it approaches a vertical asymptote. Hence, we take the limit. $\displaystyle\lim_{c\to2^-}\int_0^2\frac{7}{2-x}dx=\lim_{c\to2^-}-7\left[\ln|2-x|\right]_0^c$. Unfortunately, the limit does not exist, as $\lim_{c\to2^-}\ln|2-c|$ approaches infinity. The integral $\fbox{diverges}$.
