improper integration

[logistic_guy]

here is the question

Solve \(\displaystyle \int_{-1}^{1}\frac{1}{x}dx\).


my attemb
\(\displaystyle \int_{-1}^{1}\frac{1}{x}dx = \ln x\big|_{-1}^{1} = \ln 1 - \ln -1 = 0 - \ln -1\)
if i evaluate \(\displaystyle \ln - 1\) in my calculator i get error
what i do wrong?

 

[Dr.Peterson]

here is the question

Solve \(\displaystyle \int_{-1}^{1}\frac{1}{x}dx\).


my attempt
\(\displaystyle \int_{-1}^{1}\frac{1}{x}dx = \ln x\big|_{-1}^{1} = \ln 1 - \ln -1 = 0 - \ln -1\)
if i evaluate \(\displaystyle \ln - 1\) in my calculator i get error
what i do wrong?

What did you do wrong? Just about everything!

What does it mean that this is an improper integral?

What is the domain of the logarithm? (The calculator knows, and so should you.)

And what is the integral of 1/x? Look it up, don't just vaguely recall it!

 

[khansaheb]

he domain into two there is the question

Solve \(\displaystyle \int_{-1}^{1}\frac{1}{x}dx\).


my attemb
\(\displaystyle \int_{-1}^{1}\frac{1}{x}dx = \ln x\big|_{-1}^{1} = \ln 1 - \ln -1 = 0 - \ln -1\)
if i evaluate \(\displaystyle \ln - 1\) in my calculator i get error
what i do wrong?

(1/x) loses continuity at x= 0.

Thus you have to integrate by splitting domain into two parts.

 

[logistic_guy]

What did you do wrong? Just about everything!

What does it mean that this is an improper integral?

i think it mean we've finite undefined points in the domain of integration

What is the domain of the logarithm? (The calculator knows, and so should you.)

i think \(\displaystyle >0\)

And what is the integral of 1/x? Look it up, don't just vaguely recall it!

i already do it \(\displaystyle \ln x\)

(1/x) loses continuity at x= 0.

Thus you have to integrate by splitting domain into two parts.

i feel there's something wrong in my answerhow to split?

 

[topsquark]

i think it mean we've finite undefined points in the domain of integration


i think \(\displaystyle >0\)


i already do it \(\displaystyle \ln x\)


i feel there's something wrong in my answerhow to split?

This is basic Calculus I. Look it up in your textbook.

-Dan

 

[Dr.Peterson]

i already do it \(\displaystyle \ln x\)

Once again, have you looked it up to see if you might be wrong??

Lists of integrals - Wikipedia

en.wikipedia.org

Do you see what you are omitting? can you see why this answer is better than yours?

 

[fresh_42]

We can show you the paths to your problems' solutions, but we cannot understand them for you. Maybe you should solve one question after the other instead of posting dozens of them in very different fields all at once. It requires practice. Quantity isn't really helpful.