Evaluate the Triple Integral $\iiint _ { E } y d V$

question 108

Multiple Choice

Evaluate the triple integral $\iiint _ { E } y d V$ , where E is the solid bounded by the coordinate planes and the plane 2x + y + z = 4.

• A)1
• B) \(\frac { 3 } { 16 }\)
• C) \(\frac { 8 } { 3 }\)
• D) \(\frac { 3 } { 8 }\)
• E) \(\frac { 2 } { 3 }\)
• F) \(\frac { 16 } { 3 }\)
• G) \(\frac { 32 } { 3 }\)
• H) \(\frac { 3 } { 32 }\)

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Definitions:

Spotted Horses

Refers to prehistoric cave paintings, notably in the Lascaux Cave in France, where horses are depicted with spotted patterns on their coats, suggesting early human interaction with these animals.

Negative Handprints

Prehistoric cave art involving the application of pigment around a hand placed against a surface, leaving a silhouette or "negative" image of the hand.

Unifying Device

An element in art or literature that serves to bring together various components of the work, creating a cohesive and harmonious whole.

Cave Painting

Prehistoric art found on cave walls or ceilings, primarily depicting animals and human figures, representing some of the earliest forms of human expression.