Solve the Problem $\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 7 - x } \int _ { 0 } ^ { 10 - y - x } d x d y d z$

question 117

Multiple Choice

Solve the problem.
-Write an iterated triple integral in the order dx dy dz for the volume of the rectangular solid in the first octant bounded by the planes x = 4, y = 7, and z = 10.

• A) \(\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 7 - x } \int _ { 0 } ^ { 10 - y - x } d x d y d z\)
• B) \(\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { 10 } \mathrm { dx } d y \mathrm { dz }\)
• C) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 7 - x } \int _ { 0 } ^ { 4 - y }\)
• D) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { 4 } \mathrm { dx } d y \mathrm { dz }\)

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Definitions:

Agreeableness

Agreeableness is a personality trait characterized by warmth, kindness, and a tendency to cooperate and seek social harmony.

Extraversion

A personality trait characterized by outgoing, sociable, and energetic behavior.

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An individual's overall subjective emotional evaluation of their own worth or personal value.

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A personality trait involving excessive preoccupation with oneself, a need for admiration, and a lack of empathy for others.