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Reduction formula, integration problem 
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#1
Oct1608, 04:46 AM

P: 117

1. The problem statement, all variables and given/known data
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]^{n2}[/tex] x sec[tex]^{2}[/tex] x dx =>tan[tex]^{n1} x/n 1[/tex] 3. 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 


#2
Oct1608, 04:58 AM

Emeritus
Sci Advisor
PF Gold
P: 9,781

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
Oct1608, 05:09 AM

P: 117

Ah...I see, so that's how the sec^2 x gets canceled out.
Thanks hootenanny! 


#4
Oct1608, 05:23 AM

Emeritus
Sci Advisor
PF Gold
P: 9,781

Reduction formula, integration problem



#5
Oct1608, 09:41 AM

Mentor
P: 21,215

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
Oct1608, 09:46 AM

Mentor
P: 21,215

disce quasi semper victurus vive quasi cras moriturus speak? almost always of victory? live almost ?? (you?) die Thanks 


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