# Reduction formula, integration problem

by JFonseka
Tags: formula, integration, reduction
 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 =>$$\int$$ tan$$^{n-2}$$ x sec$$^{2}$$ x dx =>tan$$^{n-1} x/n -1$$ 3. The attempt at a solution My question is, what happened to the sec$$^{2}$$ x in the integration process? I see the tan got integrated, but I can't figure out how sec disappears
 Emeritus Sci Advisor PF Gold P: 9,772 Notice that $$\frac{d}{dx}\tan x = sec^2x$$ $$\Rightarrow dx = \frac{d\left(\tan x\right)}{\sec^2 x}$$
 P: 117 Ah...I see, so that's how the sec^2 x gets canceled out. Thanks hootenanny!
Emeritus
PF Gold
P: 9,772
Reduction formula, integration problem

 Quote by JFonseka Ah...I see, so that's how the sec^2 x gets canceled out. Thanks hootenanny!
A pleasure.
 Mentor P: 21,313 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.
Mentor
P: 21,313
 Quote by Hootenanny 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
Emeritus