Ava-May Nelson

2021-10-28

Evaluate the integral.

${\int}_{0}^{2}\frac{7}{x-2}dx$

Obiajulu

Skilled2021-10-29Added 98 answers

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,

${\int}_{0}^{2}\frac{7}{x-2}dx$

$=7{\left[\mathrm{ln}|x-2|\right]}_{0}^{2}$

$=7(\mathrm{ln}|2-2|-\mathrm{ln}|0-2|)$

$=7(\mathrm{ln}0-\mathrm{ln}|-2|)$

$=7\mathrm{ln}0$

Since$\mathrm{ln}0$ is undefined therefore the given integral cannot converge and hence is divergent.

Given definite integral is:

We have to determine whether the above integral converges or diverges.

Step 2

Then we get,

Since