Find the Integral $\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t$

question 38

Multiple Choice

Find the integral $\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t$ .

• A) \(4 \mathbf { i } + 12 t \mathbf { j } + \mathbf { C }\)
• B) \(4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } + \mathbf { C }\)
• C) \(2 t ^ { 2 } \mathbf { i } + 2 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }\)
• D) \(4 t ^ { 2 } \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }\)

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Definitions:

Perfectly Competitive Market

A market structure characterized by numerous small firms, identical products, and easy entry and exit, leading to a situation where no single firm can influence market prices.

Average Total Cost

The total cost of production divided by the quantity of output produced; encompasses both fixed and variable costs.

Long-run Equilibrium

A state where all the factors of production in an economy are being used in the most efficient way, leading to a situation where there is no tendency for change.

Perfectly Competitive Market

An economic model marked by a multitude of buyers and sellers, with no barriers to entering or leaving, and identical products.