Finding the Integral of xdx on Arc C

[SelHype]

Homework Statement

Let C be the arc of y=x² from (0,0) to (1,1). Evaluate \intxdx

Homework Equations

C1:
x=t
y=t²
-1 \leq t \leq 1 so -1 \leq x \leq 1

The Attempt at a Solution

dx is x' dt, right?

For some reason, I just can't figure this out. Any help?

 

[gabbagabbahey]

ummm \int x dx is not even a line integral; it's just an ordinary integral...do you mean \int_{\mathcal{P}} \vec{x} \cdot \vec{ds}?

 

[SelHype]

No, that is what he has down...Except the C is where the p is on yours. I did not know how to do that. I figured it out, though.

since dx=xdt and x=t,

\int from 0 to 1 of t²dt is 1/3.