Use the Shell Method to Set Up and Evaluate the Integral

question 53

Multiple Choice

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. $y = 10 - x , y = 0 , x = 0$

• A) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 10 + y ) d y = \frac { 5000 } { 3 } \pi\)
• B) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( - y ) ( 10 + y ) d y = \frac { 5000 } { 3 } \pi\)
• C) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 10 - y ) d y = \frac { 500 } { 3 } \pi\)
• D) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 10 + y ) d y = \frac { 1000 } { 3 } \pi\)
• E) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 10 - y ) d y = \frac { 1000 } { 3 } \pi\)

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Definitions:

Selective Attention

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Dissociative Identity Disorder

A psychological disorder characterized by the presence of two or more distinct personality states or identities in a single individual, each with its own patterns of perceiving and interacting with the environment.

Multiple Personality

A psychological disorder, now more commonly referred to as dissociative identity disorder (DID), characterized by the presence of two or more distinct personality states or identities within a single individual.

Chronic Schizophrenia

A long-term form of schizophrenia characterized by persistent symptoms, such as delusions and hallucinations, often leading to significant impairment.