Integrating a Logarithmic Function: How to Solve a Tricky Definite Integral

In summary, the integral ##\int -1 to 1 log((2-x)/(2+x)) dx## can be simplified using the logarithmic identity ##log\frac{a}{b} = log(a)-log(b)##. After applying this identity and integrating, the final answer is ##2log(2)##.
  • #1
Hysteria X
21
0

Homework Statement


Evaluate:

##\int -1 to 1 log((2-x)/(2+x)) dx##

Homework Equations



imgFig2.gif

The Attempt at a Solution



okay so normal attempt at integration won't work coz then we get log 1
what am i supposed to do i tried applying some general formulas of definite integral but i don't seem to get the answer :confused:
 
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  • #2
Hysteria X said:

Homework Statement


Evaluate:

##\int -1 to 1 log((2-x)/(2+x)) dx##



Homework Equations



imgFig2.gif


The Attempt at a Solution



okay so normal attempt at integration won't work coz then we get log 1
what am i supposed to do i tried applying some general formulas of definite integral but i don't seem to get the answer :confused:

Can you show what you did using normal integration? I actually don't think log(1) is really wrong. But how did you get it?
 
  • #3
This logarithmic identity should get you going:

## log\frac{a}{b} = log(a)-log(b) ##

I agree with Dick though, you have the correct answer.
 

Related to Integrating a Logarithmic Function: How to Solve a Tricky Definite Integral

What is meant by "stuck with this integration"?

"Stuck with this integration" refers to being unable to change or modify the integration between different systems or processes that have been previously implemented.

What are some potential consequences of being stuck with an integration?

Some potential consequences include reduced efficiency, increased costs, and difficulties in adapting to changing business needs.

How can one prevent getting stuck with an integration?

Careful planning and consideration of all potential factors before implementing an integration can help prevent getting stuck with it. Regular evaluation and monitoring of the integration can also help identify and address any issues before they become major problems.

What are some strategies for dealing with being stuck with an integration?

Some strategies include finding workarounds, seeking out alternate solutions, and exploring potential ways to modify or improve the integration.

How can being stuck with an integration be turned into a learning opportunity?

Being stuck with an integration can provide valuable lessons for future integration projects. By identifying and understanding the reasons for being stuck, one can learn how to avoid similar issues in the future and improve overall integration processes.

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