$$
 {\rm Work\ } 
     \quad = \quad 
                 {\int{ \vec{F} \cdot \vec{dx} } }  
     \quad = \quad 
                 F \cos(\theta) \ {\int{ {dx} } }  
$$

$$
 {\rm Work\ } 
     \quad = \quad 
                 {\int{ \vec{F} \cdot \vec{dx} } }  
     \quad = \quad 
                 F {\int{ {dx} } }  
$$

$$
 {\rm Work\ } 
     \quad = \quad 
                 {\int{ \vec{F} \cdot \vec{dx} } }  
     \quad = \quad 
                  \pm {\int{ F {dx} } }  
$$


$$
   {\rm Work\ } = F d 
$$

$$
  {F_g}  =  m g
$$

$$
  {F_g} = {{G M_1 M_2} \over{r^2}} 
$$

$$
  {\rm Work\ by\ gravity\ } = { \int_{R_E}^{R_E + H} 
            \left( {{G M_E m_{F}} \over{x^2}} \ \ (-\hat{i}) \right) 
                   \cdot 
            \left( {dx} \ \ \hat{i} \right)  }
$$

$$
  {\rm Work\ by\ Joe\ } = { \int_{R_E}^{R_E + H} 
            \left( {{G M_E m_{F}} \over{x^2}} \ \ (\hat{i}) \right) 
                   \cdot 
            \left( {dx} \ \ \hat{i} \right)  }
$$


$$
   {\rm Work\ } =  {\int{ F \thinspace dx } } 
$$


$$
   {\rm Work\ } =  {\int{ \vec{F} \cdot \vec{dx} } } 
$$

$$
   {\rm Force\ } \quad = \quad 
             { 500 {\rm N} \ \hat{i}  } \ \ 
             { -200 {\rm N} \ \hat{j}  } \ \ 
             { -100 {\rm N} \ \hat{k}  } 
$$


\bye
