Use the Given Transformation to Evaluate the Integral $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint \mathrm { dx } d y d z\end{aligned}$$

question 82

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint \mathrm { dx } d y d z\end{aligned}$$
where $R$ is the parallelepiped bounded by the planes $2 x + y - z = 4,2 x + y - z = 10 , - x + y + z = 6 , - x + y + z = 8$ , $- x + y + 2 z = 2 , - x + y + 2 z = 4$

• A) 8
• B) 36
• C) 72
• D) 16

---

Definitions:

Market Shares

The percentage of an industry's total sales that is earned by a particular company over a specified time period, indicating the company's size or presence in the market.

Interindustry Competition

The competitive relationship between firms or industries producing different goods or services that, while not direct substitutes, compete for the same consumer dollars.

Power Transmission

The process of transferring energy from its source to a location where it is used to perform work, typically involving electricity.

Homogeneous Oligopoly

A market structure where a few firms offer products or services that are virtually indistinguishable from one another.