Triangle that has the hypo as √(u^2 +1)

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Homework Help Overview

The discussion revolves around a triangle with a hypotenuse expressed as √(u² + 1), an adjacent side of length 1, and an opposite side of length u. The original poster attempts to solve an integral using trigonometric substitution.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster discusses their approach involving trigonometric substitution and expresses confusion regarding back substitution, particularly when dealing with the double angle in their integral result.

Discussion Status

Some participants provide guidance on using trigonometric identities to express functions in terms of θ rather than 2θ. The conversation reflects an exploration of the original poster's understanding and the implications of their approach.

Contextual Notes

There is a request for clarity in communication, indicating that the original poster's questions may not have been fully articulated. The nature of the problem suggests a focus on integral calculus and trigonometric identities.

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Homework Statement



If I have a triangle that has the hypo as √(u^2 +1)
adj as 1 and oppo as u
I did an integral with trig sub. So I used


Homework Equations



u = tan(θ)

The Attempt at a Solution


At the end of my integral I ended up with an expression (1/4)sin(2θ)
When I substitute back into the integral for theta. I will get (1/2)(u/(sqrt(u^2 +1))
right? How does back sub work if you have 2(theta)
 
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Use ##\sin 2\theta = 2 \sin \theta \cos \theta##. You need the trig functions in terms of ##\theta##, not ##2\theta##.
 
Always like this? With double angle?
 
Could you please use complete sentences? I'm not sure what you're asking.
 
Nevermind thx
 

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