The discussion revolves around the integration of the function \(\int_{0}^{1}\sqrt{\frac{4x^2-4x+1}{x^2-x+3}}dx\), focusing on techniques for evaluating definite integrals, particularly through substitution and manipulation of the integrand.
The discussion is ongoing, with some participants providing guidance on potential methods for simplifying the integral. The original poster has acknowledged confusion but has also indicated a clearer understanding after receiving feedback.
There is mention of changing limits of integration, which has contributed to the original poster's confusion. The discussion includes considerations of the absolute value of expressions within the integral, particularly around the point where \(2x-1\) changes sign.
I see no reason to do that.rocophysics said:Complete the square in both numerator and denominator, then use a u-sub for the radican.
\sqrt{x^2}= |x| and 2x- 1 changes sign at x= 1/2. This integral is the same assinClair said:Homework Statement
Integrate \int_{0}^{1}\sqrt{\frac{4x^2-4x+1}{x^2-x+3}}dx
Homework Equations
The Attempt at a Solution
U sub: let u=x^2-x+3 Then du=2x-1 and then have to evaluate \int_{3}^{3}\sqrt{\frac{du^2}{u}}dx But how with these limits of integration should this be 0? Not sure how to evaluate this...