remolatg

2021-11-09

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

${\int}_{0}^{5}\frac{10}{x}dx$

liannemdh

Skilled2021-11-10Added 106 answers

Step 1

Given,

${\int}_{5}^{10}\frac{10}{x}dx$

This is improper integral,

So we can write it as,

${\int}_{5}^{10}\frac{10}{x}dx=\underset{t\to 0}{lim}{\int}_{t}^{5}\frac{10}{x}dx$

$\int}_{5}^{10}\frac{10}{x}dx=\underset{t\to 0}{lim}{\left[10\mathrm{ln}\left(x\right)\right]}_{t}^{5$

$\int}_{5}^{10}\frac{10}{x}dx=-\mathrm{\infty$

$\int}_{5}^{10}\frac{10}{x}dx=-\mathrm{\infty$

Step 2

Therefore,

${\int}_{5}^{10}\frac{10}{x}dx$ diverges

Given,

This is improper integral,

So we can write it as,

Step 2

Therefore,

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