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

question 61

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:

Machine-Hours

This refers to the total number of hours that machinery is in operation, used as a basis for allocating manufacturing overhead to products.

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead costs to products or job orders, calculated before the period begins based on estimated overhead and activity levels.

Machine-Hours

Rephrased: The total hours that machinery is in operation during a specific period, used as a basis for allocating manufacturing overhead costs.

Predetermined Overhead Rate

A rate calculated to estimate the manufacturing overhead cost per unit of production activity, aiding in budgeting and cost control.