If $\mathbf { r } ( t ) = 5 \mathbf { i } + 3 t \cos \pi \mathbf { j } + 4 \sin \pi t \mathbf { k }$

question 7

Multiple Choice

If $\mathbf { r } ( t ) = 5 \mathbf { i } + 3 t \cos \pi \mathbf { j } + 4 \sin \pi t \mathbf { k }$ , evaluate $\int _ { 0 } ^ { 1 } r ( t ) d t$ .

• A) \(5 \mathbf { i } - \frac { 6 } { \pi ^ { 2 } } \mathbf { j } - \frac { 1 } { \pi } \mathbf { k }\)
• B) \(\mathbf { i } - \frac { 6 } { \pi ^ { 2 } } \mathbf { j } + \frac { 1 } { \pi } \mathbf { k }\)
• C) \(\mathbf { i } + \frac { 6 } { \pi ^ { 2 } } \mathbf { j } - \frac { 8 } { \pi } \mathbf { k }\)
• D) \(5 \mathbf { i } - \frac { 6 } { \pi ^ { 2 } } \mathbf { j } + \frac { 8 } { \pi } \mathbf { k }\)
• E) \(5 \mathbf { i } + \frac { 6 } { \pi ^ { 2 } } \mathbf { j } + \frac { 8 } { \pi } \mathbf { k }\)

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Definitions:

Reliable Measurement

Reliable measurement implies that the information or data provided is accurate, consistent, and can be dependably used for financial reporting and analysis.

Asset Recognition

The process in accounting to acknowledge and report an item as an asset on the balance sheet provided it meets certain criteria.

Residual Value

The estimated value that an asset will realize upon its sale at the end of its useful life.

Material Amount

A sum of money that is large enough to influence the economic decisions of users based on the financial statements of an entity.