# Line Integral

1. Dec 9, 2008

### SelHype

1. The problem statement, all variables and given/known data
Let C be the arc of y=x2 from (0,0) to (1,1). Evaluate $$\int$$xdx

2. Relevant equations
C1:
x=t
y=t2
-1 $$\leq$$ t $$\leq$$ 1 so -1 $$\leq$$ x $$\leq$$ 1

3. The attempt at a solution

dx is x' dt, right?

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

Last edited: Dec 9, 2008
2. Dec 9, 2008

### gabbagabbahey

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

3. Dec 10, 2008

### 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.