Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

Short Answer

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $\mathbf { F } ( x , y , z ) = x ^ { 2 } \mathbf { i } + x y \mathbf { j } + z ^ { 2 } \mathbf { k }$ , and the curve $C$ is given by the vector function $\mathbf { r } ( t ) = \sin t \mathbf { i } + \cos t \mathbf { j } + t ^ { 2 } \mathbf { k } , \quad 0 \leq t \leq \frac { \pi } { 2 }$ .