Evaluate the definite integral

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Homework Help Overview

The discussion revolves around evaluating the definite integral of the function \(\frac{1+\cos^{2}(x)}{\cos^{2}(x)}\) from 0 to \(\frac{\pi}{4}\). The subject area includes integral calculus and trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use u-substitution, split the integral into two fractions, and apply a trigonometric identity. Some participants question the effectiveness of these methods and inquire about the results of the fraction splitting.

Discussion Status

Participants are actively discussing the integration of the term \(\frac{1}{\cos^{2}(x)}\) and its recognition as a standard integral. There is acknowledgment of the challenges faced by the original poster, and some guidance is provided regarding the integral's identity.

Contextual Notes

There is a mention of the original poster's feeling of difficulty compared to previous problems, suggesting a potential gap in understanding or recall of integral calculus concepts.

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Homework Statement


[itex]\int^{\frac{\pi}{4}}_{0}\frac{1+cos^{2}(x)}{cos^{2}(x)}[/itex]

Homework Equations


The Attempt at a Solution



I tried u-sub, splitting it up into 2 fractions, and a trig identity (cos^2x=(1+cos2x)/2).
Am i missing something? The other problems were quite easy.
 
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What did you get if you split it up in two fractions? Why didn't it work?
 
I got two fractions, 1/cos^2(x) and cos^2(x)/cos^2(x)=1

I wasn't sure how to integrate the 1/cos^2(x)
 
Wow, see what happens when I take a summer off?
Thanks a lot.
 

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