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Chapter 13: Q 8. (page 1014)

Which of the iterated integrals in Exercises below could correctly

be used to evaluate the double integral:

∫26∫14f(x,y)dxdy

Short Answer

Expert verified

The iterated integral will give correct value of∬Rf(x,y)dA.

Step by step solution

01

Given Information

Rectangular region is bounded by linesx=1,x=4,y=2andy=6.

02

Simplification

Consider integral ∫26∫14f(x,y)dxdy

For type II region, integration is done wrt xfirst and then wrt y, Inner integral is solved wrt x.

In ∫26∫14f(x,y)dxdyalso, inner integral is wrt x.

Hence, iterated integral will give correct value of∬Rf(x,y)dA

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Most popular questions from this chapter

In Exercises 61–64, let R be the rectangular solid defined by

R=(x,y,z)|0≤a1≤x≤a2,0≤b1≤y≤b2,0≤c2≤z≤c2.

Assume that the density of R is uniform throughout.

(a) Without using calculus, explain why the center of

mass is a1+a22,b1+b22,c1+c22.

(b) Verify that a1+a22,b1+b22,c1+c22is the center of mass by using the appropriate integral expressions.

Find the masses of the solids described in Exercises 53–56.

The solid bounded above by the hyperboloid with equation z=x2-y2 and bounded below by the square with vertices (2, 2, −4), (2, −2, −4), (−2, −2, −4), and (−2, 2, −4) if the density at each point is proportional to the distance of the point from the plane with equationz = −4.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

∫∫R(x-ey)dAWhereR={(x,y)|-3≤x≤2,-2≤y≤2}

State Fubini's theorem.

Evaluate the triple integrals over the specified rectangular solid region.

∭R zsin⁡xcos⁡ydV,whereR=(x,y,z)∣0≤x≤π,3π2≤y≤2π,and1≤z≤3
See all solutions

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