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

question 27

Multiple Choice

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

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

---

Definitions:

Straight-Line Depreciation

A process for breaking down the expenditure of a solid asset throughout its useful life in identical yearly quotas.

Discount Factor

A multiplier used to determine the present value of future cash flows by accounting for time and interest.

Capital Budgeting

It refers to the process by which companies evaluate and select major investment projects, considering their potential long-term profitability.

After-Tax Discount Rate

The rate of return on an investment after accounting for taxes.