calculate the work done bay the field $ \vec{F} $ to move a particle along the parabolic arc $y=x^{2}$

Question

Where $x$ ranges from $0$ to $1$ for $F(x,y) = \dfrac{1}{1+x^{2}} \; \vec{j}$

Answer 1

Your curve is given by $c(t)=(t,t^2)$ for $t \in [0,1]$. Then you have to compute

$\int_{c}F(x,y)*d(x,y)=\int_{0}^1 F(c(t)) *c'(t)dt$.

Your turn !