The discussion revolves around evaluating the integral of the expression (2 - 3x/(Sqrt.(1 - x^2))) dx, which involves concepts from calculus, specifically integration techniques.
There is an ongoing exploration of different substitution methods to tackle the integral. Participants have provided varying suggestions, indicating a productive exchange of ideas without reaching a consensus on the best approach.
Some participants express confusion about the initial attempts and the appropriateness of different substitution methods, highlighting the complexity of the integral involved.
Looks like a natural for trig substitutions for both integralsFuturEngineer said:Homework Statement
Evaluate
Integrate (2-3x/(Sqrt.(1 - x^2))) dx
Homework Equations
1/Sqrt.(1-x^2) = arctan
The Attempt at a Solution
I am so lost, but this is what I've tried, but didn't work...
I separated the integral into two so
Integral of (2/(Sqrt.(1-x^20))) dx - integral of (3x/(Sqrt.(1-x^2))) dx
I am not sure how to proceed? Help! [/B]
A trig substitution would work, but I agree that an ordinary substitution (as you suggest) would be easier, which makes it a better choice.HallsofIvy said:I would NOT use a trig substitution for \frac{3x}{\sqrt{1- x^2}}. Instead let u= 1- x^2