Evaluate the Integral A) $6 \mathbf { i } - 45 \mathrm { j } + \frac { 9 } { 10 } \mathrm { k }$

question 44

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 3 } \left[ \left( \frac { 3 } { \sqrt { 1 + t } } \right) i - \left( 5 t ^ { 2 } \right) j + \left( \frac { 12 t } { \left( 1 + t ^ { 2 } \right) ^ { 2 } } \right) k \right] d t$$

• A) \(6 \mathbf { i } - 45 \mathrm { j } + \frac { 9 } { 10 } \mathrm { k }\)
• B) \(3 \mathbf { i } - 45 \mathrm { j } + \frac { 27 } { 5 } \mathbf { k }\)
• C) \(6 \mathbf { i } - 45 \mathbf { j } + \frac { 27 } { 5 } \mathbf { k }\)
• D) \(6 \mathbf { i } + 45 \mathbf { j } + \frac { 9 } { 10 } \mathbf { k }\)

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Definitions:

Conversion

The process of changing a reactant to a product through a chemical reaction, often quantified in terms of yield or efficiency.

Reagents

Substances or compounds that are added to a system to bring about a chemical reaction or are used to test for the presence of specific substances.

Following

Pertains to the act or process of coming after something in sequence or in time.

Ethyl Propanoate

A compound formed by the esterification of propanoic acid and ethanol, known for its fruity odor.