Use Cylindrical Coordinates to Evaluate the Triple Integral $$\iiint _ { E } y d V$$

question 9

Short Answer

Use cylindrical coordinates to evaluate the triple integral
$$\iiint _ { E } y d V$$
where $E$ is the solid that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 3$ and $x ^ { 2 } + y ^ { 2 } = 7$ above the $x y$ -plane and below the plane $z = x + 4$ .

---

Definitions:

Panama Canal Zone

The small strip of land on either side of the Panama Canal. The Canal Zone was under U.S. control from 1903 to 1979 as a result of Theodore Roosevelt’s assistance in engineering a coup in Colombia that established Panama’s independence.

International Progressivism

A political and social movement that advocates for reforms on a global scale, focusing on issues like environmental protection, human rights, and economic inequality.

Liberal Internationalism

A foreign policy doctrine that argues for the role of cooperation and democracy in international relations, often associated with the promotion of global peace and justice.

Western Civilization

A term referring to the cultures, institutions, and history emerging from Europe, particularly influential in shaping global development through its exploration, colonization, and cultural exchange.