Evaluate the Integral A) $\frac { 3 e ^ { 4 } + 1 } { 16 } \mathbf { j } + \frac { 5 } { 24 } \mathbf { k }$

question 20

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 1 } \left[ \frac { 1 } { \sqrt { 2 t - t ^ { 2 } } } i + t e ^ { 4 } t j - \frac { 15 t ^ { 2 } } { \left( 4 + 5 t ^ { 3 } \right) ^ { 2 } } \mathbf { k } \right] d t$$

• A) \(\frac { 3 e ^ { 4 } + 1 } { 16 } \mathbf { j } + \frac { 5 } { 24 } \mathbf { k }\)
• B) \(\frac { \pi } { 2 } \mathrm { i } + \frac { 3 \mathrm { e } ^ { 4 } + 1 } { 16 } \mathrm { j } - \frac { 5 } { 36 } \mathbf { k }\)
• C) \(- \frac { 3 } { 2 } \pi \mathbf { i } + \frac { 3 \mathrm { e } ^ { 4 } + 1 } { 16 } \mathbf { j } + \frac { 5 } { 4 } \mathbf { k }\)
• D) \(- \frac { 3 } { 2 } \pi \mathbf { i } + \frac { 3 \mathrm { e } ^ { 4 } } { 16 } \mathbf { j } + \frac { 5 } { 24 } \mathbf { k }\)

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