Use the Given Transformation to Evaluate the Integral Where $R$ Is the Parallelepiped Bounded by the Planes

question 331

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint ( 2 x + y - z ) ( z - x + y ) ( 2 z - x + y ) d x d y d z\end{aligned}$$
where $R$ is the parallelepiped bounded by the planes $2 x + y - z = 2,2 x + y - z = 3 , - x + y + z = 2 , - x + y + z = 6$ , $- x + y + 2 z = 2 , - x + y + 2 z = 7$

• A) 2700
• B) 300
• C) 1200
• D) 1350

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Definitions:

Landslide

A mass movement of rock, earth, or debris down a slope due to gravity.

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The force exerted by something against a surface, usually measured in units such as Pascal (Pa) or pounds per square inch (psi).

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A type of lava originating from the mantle, characteristically dark and rich in magnesium and iron, with low viscosity.

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A shield volcano is a type of volcano with broad, gently sloping sides and nearly circular base, formed by the eruption of low-viscosity lava that can flow a great distance from the vent.