Let ${ \vec { F } } = x \vec { i } + y \vec { j }$

question 35

Multiple Choice

Let ${ \vec { F } } = x \vec { i } + y \vec { j }$ .Write down an iterated integral that computes the flux of $\vec { F }$ through S, where S is the part of the surface $z = x ^ { 2 } + y ^ { 2 }$ below the plane z = 16, oriented downward.

• A) \(\int _ { - 4 } ^ { 4 } \int _ { - \sqrt { 16 - x ^ { 2 } } } ^ { \sqrt { 16 - x ^ { 2 } } } 2 \left( x ^ { 2 } + y ^ { 2 } \right) d y d x\)
• B) \(- \int _ { - 4 } ^ { 4 } \int _ { - \sqrt { 16 - x ^ { 2 } } } ^ { \sqrt { 6 - x ^ { 2 } } } 2 \left( x ^ { 2 } + y ^ { 2 } \right) d x d y\)
• C) \(\int _ { 0 } ^ { 4 } \int _ { - \sqrt { 16 - x ^ { 2 } } } ^ { \sqrt { 16 - x ^ { 2 } } } 2 \left( x ^ { 2 } + y ^ { 2 } \right) d y d x\)
• D) \(- \int _ { - 4 } ^ { 4 } \int _ { - \sqrt { 16 - x ^ { 2 } } } ^ { \sqrt { 16 - x ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) d y d x\)
• E) \(\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \sqrt { 16 - x ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) d y d x\)

---

Definitions:

Erikson's Eighth

Refers to the final stage in Erik Erikson's theory of psychosocial development, focused on integrity vs. despair, usually occurring in late adulthood.

Integrity Versus Despair

A stage in Erik Erikson's theory of psychosocial development, occurring in late adulthood, where individuals reflect on their life and either come to terms with it or experience regret.

Development

The process of growth and change that humans undergo throughout their life, encompassing physical, cognitive, and social aspects.

Older Adults

Individuals who are in the later stages of life, often defined as being 65 years of age or older, and experiencing the physical and cognitive changes associated with aging.