Trig substitution (integration)

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Homework Help Overview

The discussion revolves around a problem involving trigonometric substitution in the context of integration, specifically focusing on how to handle constants in the expression under the square root.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to clarify the correct substitution for an integral involving a square root with a constant. They question whether to treat the expression as if it were simply (x^2-9)^(1/2) or if the presence of a coefficient requires a different approach. Other participants discuss the appropriate trigonometric function to use and confirm the substitution method.

Discussion Status

The discussion is active, with participants providing guidance on the choice of trigonometric function and addressing the need to account for coefficients in the substitution. There is a confirmation of the substitution approach, although no consensus on the complete method has been reached.

Contextual Notes

There is mention of a coefficient in front of the x^2 term that may affect the substitution process, indicating a potential area of confusion or complexity in the problem setup.

joess
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Homework Statement


30x75o8.gif


Homework Equations



The Attempt at a Solution


I'm not asking for someone to do the question for me but I was just wondering what I'm supposed to sub in. Do I put in
2pyuz2w.gif
as if it was (x^2-9)^(1/2) or do I have to do something differently if there is a constant in front of the x^2? Thanks for any help.
 
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You are correct, secant is the correct trig function to use in this case.
However the coefficient is incomplete, you need to divide out the 4 as well.
 
So is it x=(3/2)sec(theta) ?
 
That's right! :)
 

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