The discussion revolves around the integral ∫2x√(2x-3) dx, which falls under the subject area of calculus, specifically focusing on u-substitution techniques.
Participants are actively engaging with the problem, offering different substitution strategies and discussing the implications of mixing variables in the integrand. There is no explicit consensus, but guidance has been provided regarding the need for clarity in variable substitution.
Participants are navigating the complexities of substitution in integrals, including the need to express the integrand solely in terms of u after substitution. There is an acknowledgment of potential pitfalls in the integration process.
Jtechguy21 said:Sort of. u= the inside of the square root
u=2x-3
du=2dx
dx=du/2 or 1/2
∫1/2 2xu^1/2 dx
the 2's cancel out.
now it should look like
∫x*u^1/2 and integrate that. and plug in the value for u after your done integrating
Becareful, because if i remember correctly. after integrating ∫x*u^1/2
Since we have an x. you have to solve for it, and plug it in.
u=2x-3 <-Solve the x
2x-3=0 2x=3
x=3/2
SteamKing said:If u = 2x -3, then 2x = u + 3, so that your integral after substitution has only u in it.
Your integrand becomes (u+3)*SQRT(u)*du/2
You don't want an integrand which mixes x and u after substitution.