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

question 38

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

---

Definitions:

United States V. Wong Kim Ark

A landmark 1898 US Supreme Court case that established the principle of jus soli (right of the soil), granting birthright citizenship to children born in the US to foreign parents.

American Federation of Labor

An early national federation of labor unions in the United States, founded in 1886, that focused on skilled workers.

Ida B. Wells

An African American journalist, abolitionist, and feminist who led an anti-lynching crusade in the United States in the 1890s.

Economic Independence

The condition in which an entity or nation has sufficient resources to sustain its operations without relying on external support.