Find the Area of the Surface Obtained by Rotating the Curve

question 58

Multiple Choice

Find the area of the surface obtained by rotating the curve about the y-axis. $y=\frac{1}{4} x^{2}-\frac{1}{2} \ln x, 1 \leq x \leq 8$

• A) \(\frac{3 \pi}{2}\)
• B) \(\frac{10}{3}\)
• C) \(\frac{8 \pi}{3}\)
• D) \(\frac{11 \pi}{2}\)
• E) None of these

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Definitions:

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The level of serotonin, a neurotransmitter in the brain that affects mood, emotions, and sleep patterns.

Depression-related Brain Circuit

Depression-related Brain Circuit involves specific pathways in the brain that are believed to play significant roles in the development and regulation of depressive symptoms.

Serotonin

A neurotransmitter whose abnormal activity is linked to depression, obsessive-compulsive disorder, and eating disorders.

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The neurotransmitter whose high activity has been shown to be related to schizophrenia.