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

  • Thread starter Thread starter Hysteria X
  • Start date Start date
  • Tags Tags
    Integration Stuck
Hysteria X
Messages
21
Reaction score
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:
 
Physics news on Phys.org
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?
 
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.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top