The discussion revolves around the proper method to graph the equation xy = 1 in the context of a cylindrical shell problem, particularly focusing on the integration process when rotating around the x-axis.
There is an ongoing exploration of the necessity for the integrand to match the variable of integration. Some participants assert that the integrand must be in terms of y when integrating with respect to y, while others express uncertainty about the implications of using different variable representations.
Participants are considering the implications of integrating with respect to y versus x, and the potential confusion arising from the different forms of the equation. There is an emphasis on ensuring clarity in variable usage during integration.
Well, if I am integrating with all y variables, shouldn't it make sense to use x = 1/y, instead of y = 1/x, so the variables match? For example, v = 2pi (Integrand Sign) f(y) dy.vela said:They aren't different. Why do you think they are?
vela said:Yes, of course. You need the integrand to be in terms of ##y## if you're integrating with respect to ##y##. Isn't this always the case? I guess I'm not sure why you'd think you could use 1/x in this case.