# How long?

1. Sep 17, 2010

### Little ant

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

2. Sep 17, 2010

### Char. Limit

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

3. Sep 17, 2010

### Little ant

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

4. Sep 17, 2010

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).

5. Sep 17, 2010

### Redbelly98

Staff Emeritus
Moderator's note: thread moved from Calculus & Analysis

6. Sep 17, 2010

### Staff: Mentor

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?

7. Sep 19, 2010

### sjb-2812

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

8. Sep 19, 2010

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.