Find $\mathbf { r } ( t )$ If $\mathbf { r } ^ { \prime } ( t ) = \sin t \mathbf { i } - \cos t \mathbf { j } + 6 t \mathbf { k }$

question 27

Multiple Choice

Find $\mathbf { r } ( t )$ if $\mathbf { r } ^ { \prime } ( t ) = \sin t \mathbf { i } - \cos t \mathbf { j } + 6 t \mathbf { k }$ and $r ( 0 ) = i + j + 5 k$ .

• A) \(( - \cos t + 2 ) \mathbf { i } + ( \sin t - 1 ) \mathbf { j } + \left( 3 t ^ { 2 } + 5 \right) \mathbf { k }\)
• B) \(( \cos t ) \mathbf { i } + ( \sin t - 1 ) \mathbf { j } + \left( 3 t ^ { 2 } + 5 \right) \mathbf { k }\)
• C) \(( \cos t ) \mathbf { i } + ( \sin t + 1 ) \mathbf { j } + \left( 3 t ^ { 2 } + 5 \right) \mathbf { k }\)
• D) \(( - \cos t + 2 ) \mathbf { i } - ( \sin t - 1 ) \mathbf { j } + \left( 3 t ^ { 2 } + 5 \right) \mathbf { k }\)
• E) \(( - \cos t + 1 ) \mathbf { i } - ( \sin t - 1 ) \mathbf { j } + \left( 3 t ^ { 2 } + 5 \right) \mathbf { k }\)

---

Definitions:

Disordered Brain

Refers to a state or condition where the brain's normal functions are disrupted, leading to psychological or neurological issues.

Electroconvulsive Therapy (ECT)

A medical treatment for severe mental illnesses where small electric currents are passed through the brain, intentionally triggering a brief seizure.

Tardive Dyskinesia

A neurological disorder characterized by involuntary, repetitive body movements, often resulting from long-term use of antipsychotic medication.

Schizophrenia

A long-term mental disorder characterized by distortions in thinking, perception, emotions, language, sense of self, and behavior.