Evaluate the Integral $\int y ^ { 3 } e ^ { - 7 y } d y$

question 353

Multiple Choice

Evaluate the integral.
- $\int y ^ { 3 } e ^ { - 7 y } d y$

• A) \(- \frac { 1 } { 7 } \mathrm { e } ^ { - 7 \mathrm { y } } \left[ \mathrm { y } ^ { 3 } + \mathrm { y } ^ { 2 } + \mathrm { y } + 6 \right] + C\)
• B) \(- \frac { 1 } { 28 } y ^ { 4 } e ^ { - 7 y } + C\)
• C) \(- \mathrm { e } ^ { - 7 \mathrm { y } } \left[ \frac { 1 } { 7 } \mathrm { y } ^ { 3 } + \frac { 3 } { 49 } \mathrm { y } ^ { 2 } + \frac { 6 } { 343 } \mathrm { y } + \frac { 6 } { 2401 } \right] + \mathrm { C }\)
• D) \(e ^ { - 7 y } \left[ \frac { 1 } { 7 } y ^ { 3 } - \frac { 3 } { 49 } y ^ { 2 } + \frac { 6 } { 343 } y - \frac { 6 } { 2401 } \right] + C\)

Identify and differentiate between various quality management and control methodologies, including ISO standards and Six Sigma.

Grasp the distinction between manufacturing and service operations, specifically in terms of productivity and customer contact.

Understand the role and impact of statistical analysis in operations management, particularly in improving quality and productivity.

Learn the strategic importance of dispatching, sequencing, and routing in streamlining operations.

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Definitions:

Deep Structure

In linguistics, the underlying syntactic structure or meaning of a sentence, as opposed to the surface structure which is how it is expressed.

Surface Structures

The outward appearance or organization of something, especially in linguistics where it refers to the specific syntax or wording of a sentence.

Transformational Grammar

A theory of grammar that focuses on how sentences can be transformed into other sentences through the application of rules.

Deep Structure

In linguistics, the underlying syntactic structure or meaning of a sentence, as opposed to its surface structure or actual spoken form.