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

question 160

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = \frac { 1 } { x + 5 } \mathbf { i } + \mathbf { j } + 6 \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { t } ^ { 7 } \mathbf { i } + \mathrm { t } ^ { 6 } \mathbf { j } + \mathrm { t } \mathbf { k } , 0 \leq \mathrm { t } \leq 1$$

• A) \(W = \ln \left( \frac { 6 } { 5 } \right) + 12\)
• B) \(W = \ln \left( \frac { 6 } { 5 } \right) + \frac { 7 } { 2 }\)
• C) \(W = \ln \left( \frac { 6 } { 35 } \right) + \frac { 7 } { 2 }\)
• D) \(W = \ln \left( \frac { 6 } { 5 } \right)\)