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Chapter 13: Q. 35 (page 1055)

Describe the three-dimensional region expressed in each iterated integral:

鈭鈭24鈥鈭26鈥鈭05鈥f(x,y,z)dydxdz

Short Answer

Expert verified

鈩={(x,y,z)鈭2鈮x鈮6,0鈮y鈮5,鈭2鈮z鈮4}

Step by step solution

01

Step 1. Given information.

We have been given a three-dimensional region:

鈭鈭24鈥鈭26鈥鈭05鈥f(x,y,z)dydxdz

We have to describe it in the iterated integral.

02

Step 2. Evaluate.

By the definition of triple integral 鈭a1a1鈥鈭b1b2鈥鈭c1c2鈥f(x,y,z)dzdydxrepresent the volume of the solid region 鈩=(x,y,z)鈭a1鈮x鈮a2,b1鈮y鈮b2,c1鈮z鈮c2

The given triple integral represents the volume of the rectangular solid given by鈩={(x,y,z)鈭2鈮x鈮6,0鈮y鈮5,鈭2鈮z鈮4}

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Most popular questions from this chapter

Explain how to construct a Riemann sum for a function of three variables over a rectangular solid.

Identify the quantities determined by the integral expressions in Exercises 19鈥24. If x, y, and z are all measured in centimeters and 蚁(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

鈭惟鈥z蚁(x,y,z)dV

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

f(x,y)=yxeyWjereR={(x,y)|1鈮x鈮e,0鈮y鈮2}

Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral鈭cd鈭abfx,ydxdy.

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
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