Evaluate the Integral $\int y ^ { 3 } e ^ { - 3 y } d y$

question 38

Multiple Choice

Evaluate the integral.
- $\int y ^ { 3 } e ^ { - 3 y } d y$

• A) \(- \mathrm { e } ^ { - 3 \mathrm { y } } \left[ \frac { 1 } { 3 } \mathrm { y } ^ { 3 } + \frac { 1 } { 3 } \mathrm { y } ^ { 2 } + \frac { 2 } { 9 } \mathrm { y } + \frac { 2 } { 27 } \right] + \mathrm { C }\)
• B) \(\mathrm { e } ^ { - 3 \mathrm { y } } \left[ \frac { 1 } { 3 } \mathrm { y } ^ { 3 } - \frac { 1 } { 3 } \mathrm { y } ^ { 2 } + \frac { 2 } { 9 } \mathrm { y } - \frac { 2 } { 27 } \right] + \mathrm { C }\)
• C) \(- \frac { 1 } { 12 } y ^ { 4 } e ^ { - 3 y } + C\)
• D) \(- \frac { 1 } { 3 } e ^ { - 3 y } \left[ y ^ { 3 } + y ^ { 2 } + y + 6 \right] + C\)

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