If $\mathbf { r } ( t ) = \mathbf { i } + t \cos \pi t \mathbf { j } + 2 \sin \pi t\mathbf { k }$

question 4

Multiple Choice

If $\mathbf { r } ( t ) = \mathbf { i } + t \cos \pi t \mathbf { j } + 2 \sin \pi t\mathbf { k }$ , evaluate $\int _ { 0 } ^ { 1 } r ( t ) d t$ .

• A) \(\mathbf { i } - \frac { 2 } { \pi ^ { 2 } } \mathbf { j } - \frac { 1 } { \pi } \mathbf { k }\)
• B) \(\mathbf { i } + \frac { 2 } { \pi ^ { 2 } } \mathbf { j } + \frac { 4 } { \pi } \mathbf { k }\)
• C) \[\mathbf { i } + \frac { 2 } { \pi ^ { 2 } } \mathbf { j } - \frac { 4 } { \pi } \mathbf { k }\]
• D) \(\mathbf { i } - \frac { 2 } { \pi ^ { 2 } } \mathbf { j } + \frac { 1 } { \pi } \mathbf { k }\)
• E) \(\mathbf { i } - \frac { 2 } { \pi ^ { 2 } } \mathbf { j } + \frac { 4 } { \pi } \mathbf { k }\)

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Definitions:

Microgram

A unit of mass equal to one millionth of a gram, often used to measure very small quantities of medication.

Liter

A unit of volume equal to 1,000 milliliters or approximately 33.814 U.S. fluid ounces.

Meter

A device used to measure something, such as electricity, gas, or in the medical field, the concentration of a substance in the blood.

Milliliters

A unit of volume in the metric system, equal to one-thousandth of a liter.