The discussion revolves around finding the length of the curve defined by the equation y² = (x-1)³, specifically from the points (1,0) to (2,1). Participants are exploring the appropriate setup for the integral to calculate the arc length.
Some participants have offered guidance on using the form y = f(x) and pointed out the significance of the starting and ending points in determining the limits of integration. However, there remains uncertainty about the correct limits and the interpretation of the coordinates.
Participants are grappling with the definitions of the points (1,0) and (2,1) and how they relate to the function being analyzed. There is a noted discrepancy in understanding the values of x and y at these points, which is affecting their approach to the problem.
EEristavi said:Homework Statement
I have to find length of the curve: y2 = (x-1)3 from (1,0) to (2,1)
Homework Equations
s = ∫ √(1 + (f '(x) )2 ) dx where we have integral from a to b
The Attempt at a Solution
I'm bit confused:
I'm thinking of writing function regarding x, f(x). However, I can also write for y, f(y).
Which is better? and what values should I take for definite integral ("limits")
Dick said:What does that tell you about limits on xxx?
EEristavi said:well, from the problem statement x should change from 0 to 1, but its not correct (as I see from the solution), integral is taken from 1 to 2 (and I can't figure it out why)
Dick said:You do know that, e.g., at the point (1,0)(1,0)(1,0) the value of xxx is 1, right?
EEristavi said:OK, now I think, I need more clarification... I will write what is in my mind:
point (1, 0) means that y=1, x=0
but I see from function y = f (x), that if x = 0 => y = 0
So I guess, here is my problem of understanding...
Ok, maybe it's been a while, since I've done some mathematics :DDick said:Where I come from the point ##(1,0)## means ##x=1## and ##y=0##. That looks like the definition the problem is using also. I don't think I've ever heard of a different convention.