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

question 206

Multiple Choice

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where F $( x , y , z ) = y z \mathbf { i } + x z \mathbf { j } + x y \mathbf { k }$ , and the curve $C$ is given by the vector function $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t \mathbf { j } + t ^ { 3 } \mathbf { k } , 0 \leq t \leq 1$ .

• A) \(- 3\)
• B)\(- 2\)
• C)\(- 1\)
• D)\(0\)
• E)\(1\)
• F)\(2\)
• G)\(3\)
• H) \(4\)

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