Evaluate the Integral $$\int _ { 0 } ^ { 4 } \left[ - \mathbf { i } - \frac { 2 t } { \left( 7 + t ^ { 2 } \right) ^ { 2 } } j + \frac { 15 } { 2 } \sqrt { t k } \right] d t$$

question 26

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 4 } \left[ - \mathbf { i } - \frac { 2 t } { \left( 7 + t ^ { 2 } \right) ^ { 2 } } j + \frac { 15 } { 2 } \sqrt { t k } \right] d t$$

• A) \(+ 4 i + \frac { 16 } { 161 } j + 40 k\)
• B) \(- 4 i - \frac { 16 } { 161 } j - 40 k\)
• C) \(- 4 i - \frac { 16 } { 161 } j + 40 k\)
• D) \(- 4 i + \frac { 4 } { 77 } j + 40 k\)

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Definitions:

Labor-force Participation Rate

The labor-force participation rate is the percentage of the working-age population that is engaged in the labor market by either being employed or actively seeking employment.

Adults Employed

The portion of the working-age population that is currently employed in the labor market.

Adults Unemployed

Individuals of working age who are without work, but are available for and seeking employment.

Adults Not in the Labor Force

Individuals over the working age who are neither employed nor actively seeking employment.