Average values Find the average temperature on that part

Chapter 11, Problem 39E

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QUESTION:

Find the average temperature on that part of the plane \(3 x+4 y+z=6\) over the square \(|x| \leq 1,|y| \leq 1\), where the temperature is given by \(T(x, y, z)=e^{-z}\)

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QUESTION:

Find the average temperature on that part of the plane \(3 x+4 y+z=6\) over the square \(|x| \leq 1,|y| \leq 1\), where the temperature is given by \(T(x, y, z)=e^{-z}\)

ANSWER:

Solution  39E

Step 1

For a function of the form, the derivative of such function is given by

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