Find the Work Done by F Over the Curve in the Direction

question 210

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = \mathrm { ti } + \frac { 1 } { 2 } \mathrm { j } + \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { e } ^ { 2 } \mathrm { t } _ { \mathbf { i } } + \mathrm { e } ^ { 2 } \mathrm { t } \mathbf { j } + \left( - 7 \mathrm { t } ^ { 2 } + \mathrm { t } \right) \mathbf { k } , - 1 \leq \mathrm { t } \leq 1$$

• A) \(W = e ^ { 2 } + e ^ { - 2 } - 12\)
• B) \(\mathrm { W } = \mathrm { e } ^ { 2 } + \mathrm { e } ^ { - 2 } + 2\)
• C) \(W = - 12\)
• D) \(W = 2\)

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