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

`(-5)/(2)\int ^0_(-\infty)(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

`(-5)/(2)\int ^0_(-\infty)(du)/(u)=(-5)/(2)\ln (u)|^0_(-\infty)`

By evaluating the last result, we have

`(-5)/(2)\int ^0_(-\infty)(du)/(u)=(-5)/(2)(\ln (0)-\ln (-\infty))`

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