Trigonometric Substitution Problem - Calculus 2

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The discussion revolves around a trigonometric substitution problem in a Calculus 2 class, specifically the integral ∫(4/√(3-2x²))dx. The original poster expresses confusion about how to approach the problem, particularly regarding factoring out coefficients in front of variables. A participant clarifies that √(3-2x²) can be expressed as √2 * √(3/2 - x²), which helps the original poster understand the substitution better. The conversation highlights the importance of recognizing how to manipulate square roots in trigonometric substitutions. The original poster plans to attempt the problem after receiving clarification.
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...

\int\frac{4}{\sqrt{3-2x^2}}dx

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

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

Yes, but \sqrt{3-2x^2} = \sqrt{2}*\sqrt{\frac{3}{2}-x^2}. I may not have been clear in my previous post.
 
Oh! Duh! Thank you!
I'll give it a try.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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