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

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

• Can you think of an integral relating work and force? Look at the 'work (physics)' wiki and you will definitely find out how to proceed. – Rumplestillskin Dec 19 '16 at 11:58
• Young man, I did not ask the question. I'm just trying to understand and / or find a way to solve. I followed your concern and continue with the same problem. If you can not help me, thank you anyway. – Felipe Maia Dec 19 '16 at 12:07
• $$\int_C{\frac{dy}{1+x^2}}=\int_0^1{\frac{2xdx}{1+x^2}}=\ln(1+x^2)|_0^1=\ln2$$ – Daniil Dec 19 '16 at 13:32
• @Daniil Thanks! – Felipe Maia Dec 19 '16 at 20:46

Your curve is given by $c(t)=(t,t^2)$ for $t \in [0,1]$. Then you have to compute
$\int_{c}F(x,y)*d(x,y)=\int_{0}^1 F(c(t)) *c'(t)dt$.