Find the Arc Length of the Curve on the Given $x = t ^ { 2 } , y = 8 t , 0 \leq t \leq 4$

question 1

Multiple Choice

Find the arc length of the curve on the given interval. $x = t ^ { 2 } , y = 8 t , 0 \leq t \leq 4$

• A) \(4 ( \sqrt { 2 } + \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )\)
• B) \(4 ( \sqrt { 2 } - \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )\)
• C) \(4 ( \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )\)
• D) \(16 ( \sqrt { 2 } - \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )\)
• E) \(16 ( \sqrt { 2 } + \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )\)

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Definitions:

Major Depressive Disorder

A mental disorder characterized by a pervasive and persistent low mood that is accompanied by low self-esteem and by a loss of interest or pleasure in normally enjoyable activities.

Diagnostic Tests

Procedures and tests used to identify the nature or cause of a health condition or disease.

Spiritual Distress

A state of suffering related to the impaired ability to experience and integrate meaning and purpose in life through connectedness with self, others, art, music, literature, nature, or a power greater than oneself.

Vegetative Signs

Physical symptoms primarily involving disruptions to sleep, eating habits, energy, and sexual activity, often associated with major depressive disorder.