Problem: Let the force field $\vec{F}$ be given by,
$$\vec{F}(\vec{x}) = \dfrac{1}{x_{1}^{2} + x_{2}^{2}} \binom{2}{4}$$
Compute the integral of the force field along the circle of radius $r$ centered at the origin.
- (a) First determine $\vec{x}(t)$ and $\dot{\vec{x}}(t)$.
- (b) Compute the integral along the curve from $E(r/0)$ to $W(-r/0)$ oriented counterclockwise.
- (c) Compute the integral along the curve from $N(0/r)$ to $S(0/r)$ oriented clockwise.
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Now I know that I have to find $\vec x(t) $ and $\vec x \dot x (t) $ And I think that I'd have to integrate $\vec F $($\vec x $) to find $\vec x(t) $. And I think I have to differentiate it to find $\vec x \dot x (t) $ I can't figure out how to do the accent here so I'll post a picture for clarity purpose.
Problem is that I can't integrate $\vec x (t) $ nor differentiate $\vec x \dot x (t) $. Is it possible to do it with 2 variables? I'd appreciate some tips you can help me.