• Support PF! Buy your school textbooks, materials and every day products Here!

Reduction formula, integration problem

  • Thread starter JFonseka
  • Start date
  • #1
117
0

Homework Statement



Part of an example of using reduction formula, I won't post the whole question as I get most of it, just at the very end, magical things happen with the working and things disappear, as they usually do with integration:

The definite integral goes from 0 to pi/4

=>[tex]\int[/tex] tan[tex]^{n-2}[/tex] x sec[tex]^{2}[/tex] x dx
=>tan[tex]^{n-1} x/n -1[/tex]

The Attempt at a Solution



My question is, what happened to the sec[tex]^{2}[/tex] x in the integration process?
I see the tan got integrated, but I can't figure out how sec disappears
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Notice that

[tex]\frac{d}{dx}\tan x = sec^2x[/tex]

[tex]\Rightarrow dx = \frac{d\left(\tan x\right)}{\sec^2 x}[/tex]
 
  • #3
117
0
Ah...I see, so that's how the sec^2 x gets canceled out.

Thanks hootenanny!
 
  • #4
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Ah...I see, so that's how the sec^2 x gets canceled out.

Thanks hootenanny!
A pleasure.
 
  • #5
33,173
4,858
Since the integral is a definite integral, you should end up with a number, or at least an expression that doesn't involve n. Your final expression can easily be evaluated at both limits of integration.

As a minor point, you're using an "implies" symbol (==>) incorrectly. The first integral doesn't "imply" the second; it's equal to it.
 
  • #6
33,173
4,858
A pleasure.
It probably has been asked before, but what's the English equivalent of your signature line? I think I understand a few of the words.

disce quasi semper victurus vive quasi cras moriturus

speak? almost always of victory? live almost ?? (you?) die

Thanks
 
  • #7
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
disce quasi semper victurus vive quasi cras moriturus

speak? almost always of victory? live almost ?? (you?) die
I'm impressed! You're quite close to the literal translation, but the meaning is

"Learn as if you were going to live forever, live as if you were going to die tomorrow".
 

Related Threads for: Reduction formula, integration problem

Replies
4
Views
6K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
7K
Replies
1
Views
2K
  • Last Post
Replies
8
Views
899
Replies
2
Views
11K
Replies
4
Views
2K
Top