Ava-May Nelson

2021-10-28

Evaluate the integral.
${\int }_{0}^{2}\frac{7}{x-2}dx$

Obiajulu

Step 1
Given definite integral is:
${\int }_{0}^{2}\frac{7}{x-2}dx$
We have to determine whether the above integral converges or diverges.
Step 2
Then we get,
${\int }_{0}^{2}\frac{7}{x-2}dx$
$=7{\left[\mathrm{ln}|x-2|\right]}_{0}^{2}$
$=7\left(\mathrm{ln}|2-2|-\mathrm{ln}|0-2|\right)$
$=7\left(\mathrm{ln}0-\mathrm{ln}|-2|\right)$
$=7\mathrm{ln}0$
Since $\mathrm{ln}0$ is undefined therefore the given integral cannot converge and hence is divergent.

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