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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James Madison

An American statesman, diplomat, expansionist, philosopher, and Founding Father who served as the fourth president of the United States from 1809 to 1817, known as the "Father of the Constitution."