13 less than two-birds of a number

Solved

Show answers

Ответ:

viridianasar5158

22.10.2020

Mathematics

So the answer is DNC(Does Not Convergence)

Step-by-step explanation:

Given;

$\int\limits^\infty_5 {\frac{7}{x^{2}-9 } } \ dx$

We know,

The integral is an improper integral because the upper limit of integration approaches infinity. First, replace the infinite upper limit by the finite limit 'l' and take the limit of 'l' to approach infinity.

$\int\limits^\infty_5 {\frac{7}{x^{2}-9 } } \, dx=7 \lim_{l \to \infty} \int\limits^\infty_5 {\frac{1}{x^{2}-9 } } \, dx$

$7 \lim_{l \to \infty} \int\limits^\infty_5 {\frac{1}{x^{2}-3^{2} } } \, dx$

$7\times \lim_{l \to \infty} \left [ \frac{1}{2\times 3} \log\left |\frac{x-3}{x+3} \right | \right ]_{5}^{l}$ (∵We know; $\int {\frac{1}{x^{2}-a^{2} } } \, dx= \frac{1}{2\times a} \log\left |\frac{x-3}{x+3} \right |$ )

$\frac{7}{6} \times \lim_{l \to \infty} \left[ \log\left | \frac{l-3}{l+3} \right |-\log\left | \frac{5-3}{5+3}\right |\right]$

$\frac{7}{6} \times \lim_{l \to \infty} \left[ \log\left | \frac{l-3}{l+3} \right |-\log\left | \frac{-2}{8}\right |\right]$

$\frac{7}{6} \times \left[ \log\left | \frac{\infty-3}{\infty+3} \right |-\log( \frac{2}{8})\right]$ (∵ $\left | -\frac{2}{8} \right |=(\frac{2}{8} )$ )

$\frac{7}{6} \times \left[ \infty-\log( \frac{2}{8})\right]$

$\frac{7}{6}\times \infty$

$\infty$

Thus the integral Does Not Convergence.

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice