Question

Ap Calc B.C. I think the answer is divergent because the limit approaches infinity but I’m not sure.

Answer 1

Our integral can be writen as

$\frac{-5}{2}\int ^0_{-\infty}\frac{2dx}{2x-5}$

By defining the variabl u as

$\begin{gathered} u=2x-5 \\ we\text{ have that} \\ du=2dx \end{gathered}$

then our integral can be rewriten as

$\frac{-5}{2}\int ^0_{-\infty}\frac{du}{u}=\frac{-5}{2}\ln (u)|^0_{-\infty}$

By evaluating the last result, we have

$\frac{-5}{2}\int ^0_{-\infty}\frac{du}{u}=\frac{-5}{2}(\ln (0)-\ln (-\infty))$

However, logarithm of zero and logarithm of minus infinity are undefined. So, the intergral is divergent