Set Up an Integral for the Area of the Surface $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

question 69

Multiple Choice

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
- $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

• A) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• B) \(\pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• C) \(\pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• D) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)

Understand how early experiences influence later development.

Recognize the role of cultural and historical contexts in shaping human development.

Identify methods for studying developmental changes.

Apply developmental psychology concepts to interpret human behaviors at different life stages.

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Definitions:

Owning Responsibility

The act of acknowledging and accepting responsibility for one's actions or decisions.

Step 6

Refers to a specific step in various step-based recovery programs, generally involving preparation for self-improvement and rectification of wrongs.

Honesty

The quality of being truthful, transparent, and free from deceit or fraud in one's actions and statements.

Step 1

The first stage or initial point in a process or series of actions, often implying the commencement of an effort or journey.