Set Up an Integral for the Area of the Surface $x = \int _ { 0 } ^ { y } \cos t d t , 0 \leq y \leq \pi / 3 ; y \text {-axis }$

question 98

Multiple Choice

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
- $x = \int _ { 0 } ^ { y } \cos t d t , 0 \leq y \leq \pi / 3 ; y \text {-axis }$

• A) \(\pi \int _ { 0 } ^ { \pi / 3 } \left( \int _ { 0 } ^ { y } \sin t d t \right) \cos y d y \quad\)
• B) \(- 2 \pi \int _ { 0 } ^ { \pi / 3 } \left( \int _ { 0 } ^ { y } \sin t d t \right) \cos y d y\)
• C) \(- 2 \pi \int _ { 0 } ^ { \pi / 3 } \left( \int _ { 0 } ^ { y } \cos t d t \right) \sin y d y\)
• D) \(\pi \int _ { 0 } ^ { \pi / 3 } \left( \int _ { 0 } ^ { y } \cos t d t \right) \sin y d y\)

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Definitions:

Self-concept

A person's perception and awareness of themselves, including beliefs about their own attributes, behaviors, and how they are perceived by others.

Social Comparison

The act of evaluating oneself against the abilities, status, or qualities of other people, which can influence self-esteem and motivation.

Social Reality

Social reality encompasses the norms, beliefs, and collectively agreed-upon constructs that influence how societies operate and individuals interact within them.

Self-esteem

An individual's subjective evaluation of their own worth, encompassing beliefs about personal value and competence.