Evaluate the line integral ( int_{C} mathbf{F} cdot d mathbf{r} ), where ( C ) is given by the vector function ( mathbf{r}(t) ). [ begin{array}{l} mathbf{F}(x, y, z)=(x+y) mathbf{i}+(y-z) mathbf{j}+z^{2} mathbf{k} mathbf{r}(t)=t^{2} mathbf{i}+t^{3} mathbf{j}+t^{2} mathbf{k}, 0 leq t leq 1 end{array} ]

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Evaluate the line integral  (  int_{C}  mathbf{F}  cdot d  mathbf{r}  ), where  ( C  ) is given by the vector function  (  mathbf{r}(t)  ).  [  begin{array}{l}  mathbf{F}(x, y, z)=(x+y)  mathbf{i}+(y-z)  mathbf{j}+z^{2}  mathbf{k}     mathbf{r}(t)=t^{2}  mathbf{i}+t^{3}  mathbf{j}+t^{2}  mathbf{k}, 0  leq t  leq 1  end{array}  ]

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(Solved): Evaluate the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \), where \( C \) is ...

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