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

question 20

Multiple Choice

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 $z = x + 4$ .

• A) \(8.57\)
• B) 0
• C) \(3.4\)
• D) \(9.19\)
• E) \(0.54\)

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Definitions:

Chromatin

The complex of DNA and proteins that forms chromosomes within the nucleus of eukaryotic cells, serving to package DNA into a smaller volume to fit in the cell and control gene expression.

Nucleolus

A structure located within the cell nucleus, primarily involved in the synthesis and assembly of ribosomes, essential components for protein production.

Nuclear Envelope

The double-membrane structure that encloses the nucleus of a eukaryotic cell, separating the nucleus from the cytoplasm and containing nuclear pores for transport.

Nuclear Pores

Openings in the nuclear envelope that allow the passage of ions, molecules, and RNA between the nucleus and the cytoplasm.