Trigonometric Substitution Problem - Calculus 2

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Homework Help Overview

The discussion revolves around a trigonometric substitution problem from a Calculus 2 course, specifically involving the integral of a function with a square root in the denominator.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses confusion about how to begin the problem, particularly regarding the evaluation of trigonometric substitutions with coefficients. Some participants suggest factoring out constants, while others clarify the relationship between the expressions involved.

Discussion Status

Participants are actively engaging with the problem, exploring different approaches to simplifying the expression. There is a collaborative effort to clarify misunderstandings, and one participant indicates they will attempt the problem after receiving guidance.

Contextual Notes

The original poster notes that their professor has not yet covered trigonometric substitutions involving coefficients, which may contribute to their uncertainty.

khatche4
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Hey there
This is a trig substitution for my Calculus 2 class and I really have NO idea how to get started...

[tex]\int\frac{4}{\sqrt{3-2x^2}}dx[/tex]

My professor has yet to go over how to evaluate trigonometric substitutions with coefficients in front of variables.
 
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how about factoring out the 2?
 
How would you factor out the two?

Because [tex]\sqrt{3-2x^2}[/tex] is not the same as 2*[tex]\sqrt{\frac{3}{2}-x^2}[/tex]
 
khatche4 said:
How would you factor out the two?

Because [tex]\sqrt{3-2x^2}[/tex] is not the same as 2*[tex]\sqrt{\frac{3}{2}-x^2}[/tex]

Yes, but [tex]\sqrt{3-2x^2} = \sqrt{2}*\sqrt{\frac{3}{2}-x^2}[/tex]. I may not have been clear in my previous post.
 
Oh! Duh! Thank you!
I'll give it a try.
 

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