Let S Be the Cube with Vertices $( \pm 1 , \pm 1 , \pm 1 )$

question 6

Multiple Choice

Let S be the cube with vertices $( \pm 1 , \pm 1 , \pm 1 )$ . Approximate $\iint _ { S } \sqrt { x ^ { 2 } + 2 y ^ { 2 } + 7 z ^ { 2 } }$ by using a Riemann sum as in Definition 1, taking the patches $S _ { i j }$ to be the squares that are the faces of the cube and the points $P _ { i j }$ to be the centers of the squares.

• A) \(8 ( 3 + \sqrt { 2 } )\)
• B) \(8 ( 3 + \sqrt { 7 } )\)
• C) \(8 ( 1 + \sqrt { 2 } + \sqrt { 7 } )\)
• D) \(4 ( 1 + \sqrt { 2 } + \sqrt { 7 } )\)
• E) none of these

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Definitions:

Endocrine Glands

Glands of the endocrine system that secrete hormones directly into the bloodstream to regulate various bodily functions.

Hormones

Chemical substances produced by glands in the body that regulate the activity of cells or organs, essential for every activity of life.

Endocrine Glands

Glands that secrete hormones directly into the bloodstream, regulating processes like growth, metabolism, and mood.

Hormones

Chemical messengers produced by the endocrine glands that regulate various bodily functions by traveling through the bloodstream to tissues or organs.