Absolute values in standard integrals

  • Thread starter NanakiXIII
  • Start date
  • #1
392
0
In a lot of compilations of standard integrals (my Calculus book does this, Wikipedia does this), a lot of the integrals of trigonometric functions have an absolute value in their solution which seems out of place to me. For example, take the integral

[tex]\int dx \cot{x}[/tex].

My Calculus book says this equals [tex]\log |\sin{x}|[/tex]. Now, I could be mistaken, but it seems to me that [tex]\log (\sin{x})[/tex] would do just fine and in fact, since [tex]|\sin{x}|[/tex] isn't a smooth function, I wouldn't expect to find it as a solution.

My first guess is that the [tex]| |[/tex] are for some reason used without their meaning as absolute value. Is this the case? If so, what's the point of using them instead of regular brackets?
 

Answers and Replies

  • #2
27
0
log(-x) isn't defined.
 
  • #3
392
0
You are right, of course. And the cotangent is not a bounded function, so the solution not being smooth is not so strange.
 

Related Threads on Absolute values in standard integrals

  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
3
Views
13K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
10
Views
2K
Replies
11
Views
877
Replies
1
Views
4K
Replies
3
Views
5K
Replies
1
Views
719
Replies
2
Views
9K
Top