The discussion revolves around the algebraic manipulation of the expression involving squares, specifically whether the equation \(a^2 + u^2 - 2au = (a-u)^2 = (u-a)^2\) holds true. Participants also explore the implications of this expression in the context of integrating the function \(x^{-\frac{3}{2}}\) over specific bounds.
Some participants have provided insights into the algebraic expressions, while others have raised questions about the assumptions made regarding the square root. The discussion appears to be progressing with participants sharing their work and clarifying concepts.
There is mention of the original poster's difficulty in using LaTeX due to mobile constraints, which may affect the clarity of the shared work. Additionally, the integration bounds are specified as \((a-u)^2\) to \((a+u)^2\), which may be relevant to the discussion.
Yes, these expressions are all equal.Pual Black said:
It would be helpful to see your work.Pual Black said:
I think the problem might be from taking the square root of (a - u)2. It's not necessarily equal to a - u. What is true is that ##\sqrt{(a - u)^2} = |a - u|## which in turn is equal to ##|u - a|##.Pual Black said:
