   Chapter 15, Problem 7RCC

Chapter
Section
Textbook Problem

(a) Write the definition of the triple integral of f over a rectangular box B.(b) How do you evaluate ∭ B f ( x ,   y ,     z )   d V ? (c) How do you define ∭ E f ( x ,   y ,     z )   d V ? if E is a bounded solid region that is not a box?(d) What is a type 1 solid region? How do you evaluate ∭ E f ( x ,   y ,     z )   d V ? if E is such a region?(e) What is a type 2 solid region? How do you evaluate ∭ E f ( x ,   y ,     z )   d V ? if E is such a region?(f) What is a type 3 solid region? How do you evaluate ∭ E f ( x ,   y ,     z )   d V ? if E is such a region?

(a)

To determine

To write: The definition of the triple integral of f over a given rectangular box B.

Explanation

The triple integral of f is defined using the Riemann sum for the three dimensional space. It is given by,

Bf(x,y,z)dV=liml,m,ni=1lj=1mk=1n

(b)

To determine

To evaluate: The given integral Bf(x,y,z)dV .

(c)

To determine

To define: Ef(x,y,z)dV where E is a bounded region.

(d)

To determine

To explain: The type 1 region and the method of evaluating it.

(e)

To determine

To explain: The type 2 region and the method of evaluating it.

(f)

To determine

To explain: The type 3 region and the method of evaluating it.

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