Line Length Between (0,0) & (1,1): Y=X^2

[Little ant]

How long is the line tended between points (0,0) and (1,1) if Y=X^2?

 

[Char. Limit]

How long is the line tended between points (0,0) and (1,1) if Y=X^2?

I'm not sure why y=x^2 matters, but the distance between (0,0) and (1,1) is \sqrt{2}.

 

[Little ant]

thanks, but i know that distance, i want know the long of the line.

 

[statdad]

thanks, but i know that distance, i want know the long of the line.

You just got the length of the line between the points. Do you mean this: how long is the portion of the graph of y = x^2 from x = 0 to x = 1? (That graph is not a line - that could be the cause of the confusion).

 

[Redbelly98]

Moderator's note: thread moved from Calculus & Analysis

 

[Mark44]

How long is the line tended between points (0,0) and (1,1) if Y=X^2?

If I understand what you're asking (which confused a couple of other people), you are asking about the arc length along the curve y = x² between x = 0 and x = 1. This calculation involves an integral.

What have you done to start this problem?

 

[sjb-2812]

You just got the length of the line between the points. Do you mean this: how long is the portion of the graph of y = x^2 from x = 0 to x = 1? (That graph is not a line - that could be the cause of the confusion).

Sorry, how is it not a line? Does line have some extra meaning that I'm missing?

 

[statdad]

"Sorry, how is it not a line? Does line have some extra meaning that I'm missing?"

A line is a graph generated by a linear function. The function y = x^2 is quadratic; you are looking a piece of its graph, which is a parabola.

 

[sjb-2812]

Ahh, I was thinking more "A line is a path that joins two points", regardless of generating function