Given $\vec{F} =(y^2+x^2,−2xy)$. I want to calculate the work done by this force, that is applied on a particle moving from $(0,0)$ to $(3,5)$ in a straight line.
I know that $W=\int_1^2 \vec{F} \cdot d\vec{r}$. The problem is that I don't really now how to properly express $d\vec{r}$ and the integral boundaries.
How do I write this down correctly? Is there some sort of useful parameterization (line integral over continuous vector field)?
Best Answer
Hint: With $$y=\frac53x$$ we have
$$ W=\int_0^3\left(\left[\frac53x\right]^2+x^2,-2x\left [\frac53x\right]\right)\cdot\left(1,\frac53\right)dx $$
Can you take it from here?