# Work with a line integral

1. May 6, 2009

### Breedlove

1. The problem statement, all variables and given/known data
Find the work doneby the force field F on a particle that moves along the curve C.
F(x,y)=xy i + x^2j
C: x=y^2 from (0,0) to (1,1)

2. Relevant equations

$$\int$$F dot dr=$$\int^{b}_{a}F(r(t))dotr'(t)dt$$

3. The attempt at a solution

Okay, so I parametrized x=t and y=t^2 (giving r(t)=ti+t^2j right?) and substituted those values in for x and y in F, dotted that with 1i+2tj because I think that it is the derivative of r, if the parametric equations for r are x=t and y=t^2. I then took the integral of the dot product i just took over the interval 0 to 1. I ended up with 3/4 but the correct answer is 3/5

2. May 6, 2009

### Defennder

No, the curve is x=y^2 not y=x^2 so your parametric form of y should be $$y=\sqrt{t}$$. Alternatively use: $$y=t$$ and $$x=t^2$$.