Finding Length of a Curve: y2 = (x-1)3

[EEristavi]

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]

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")

Just try it in the form $y=f(x)$. And you are given a starting point and an ending point. What does that tell you about limits on $x$?

 

[EEristavi]

What does that tell you about limits on xxx?

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]

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)

You do know that, e.g., at the point $(1,0)$ the value of $x$ is 1, right?

 

[EEristavi]

You do know that, e.g., at the point (1,0)(1,0)(1,0) the value of xxx is 1, right?

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...

 

[Dick]

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...

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.

 

[EEristavi]

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.

Ok, maybe it's been a while, since I've done some mathematics :D

Thank you :)