$\int_{-a+1}^{a+2} \frac{d x}{(a-x)}=\lim _{b \rightarrow a^{-}} \int_{-a+1}^{b} \frac{d x}{(a-x)}+\lim _{c \rightarrow a^{+}} \int_{c}^{a+2} \frac{d x}{(a-x)}$ .

Question

Quizplus · Accepted Answer

The integral on the left side is not defined at $x = a$ because the integrand becomes infinite. Splitting the integral at $x = a$ and taking limits from both sides as shown on the right side correctly handles the singularity, allowing the evaluation of the integral in a piecewise manner.