Trig sine substitution doesnt work

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Homework Help Overview

The discussion revolves around the integration of the function \(\int_{0}^{1} \sqrt{1 + 4t^2} dt\), specifically addressing the challenges encountered with trigonometric substitution. Participants express confusion regarding the applicability of sine substitution and explore alternative methods.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss various substitution methods, including trigonometric and hyperbolic substitutions. Questions arise about the effectiveness of these substitutions and the implications for integration limits.

Discussion Status

Several participants have suggested different substitution techniques, indicating a variety of approaches being explored. There is acknowledgment of the complexity of the problem, and while some guidance has been offered, there is no explicit consensus on the best method to proceed.

Contextual Notes

Participants are considering how changes in substitution might affect the limits of integration, raising questions about the correctness of their transformations. There is also mention of a potential need for further study to grasp the underlying concepts better.

stunner5000pt
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how would on integrate [tex]\int_{0}^{1} \sqrt{1 + 4t^2} dt[/tex]
trig sub sittution doesn't work since one doesn't get tan^2 +1 .

i tryed solving this with matematica and it yielded something with a sinh argument. I am not familiarwi the hyp sine substitution.
 
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Use the sustitution [itex]2t = tan \theta[/itex]. Be prepared to integrate [itex]sec^3 \theta[/itex].

Regards,
George
 
You may find that a substitution of t for sinh(theta)/2 will assist. And then you might find it useful to know how to write cosh(theta) in terms of exponentials.

Lots of ways to skin a small furry critter.

Carl
 
to make things appear simpler factor out the 4, then make the proper trig substitution; if you still don't get it, you've definitely got some more studying to do.
 
CarlB said:
Lots of ways to skin a small furry critter.
Carl

AbsolutelY!

Another way is to make the substitution [itex]2t = sinh x[/itex], and then to make a "half-angle" substitution for [itex]cosh^{2} x[/itex].

Regards,
George
 
would the limits of integration change in this process?
for t=0, theta = 0
for t =1 , theta = arctan 2
is that right?
 

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