1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivatives 5 Integration 6 Applications Of Integration 7 Integration Techniques 8 Sequences And Infinite Series 9 Power Series 10 Parametric And Polar Curves 11 Vectors And Vector-valued Functions 12 Functions Of Several Variables 13 Multiple Integration 14 Vector Calculus D1 Differential Equations D2 Second-order Differential Equations A Algebra Review expand_more
13.1 Double Integrals Over Rectangular Regions 13.2 Double Integrals Over General Regions 13.3 Double Integrals In Polar Coordinates 13.4 Triple Integrals 13.5 Triple Integrals In Cylindrical And Spherical Coordinates 13.6 Integrals For Mass Calculations 13.7 Change Of Variables In Multiple Integrals Chapter Questions expand_more
Problem 1E: 1. Write an iterated integral that gives the volume of the solid bounded by the surface f(x, y) = xy... Problem 2E: Write an iterated integral that gives the volume of a box with height 10 and base R {(x,y):0x5,2y4}. Problem 3E: Write two iterated integrals that equal Rf(x,y)dA, where R={(x,y):2x4,1y5}. Problem 4E: Consider the integral 1311(2y2+xy)dydx. State the variable of integration in the first (inner)... Problem 5E: Iterated integrals Evaluate the following iterated integrals. 5.02014xydxdy Problem 6E: Iterated integrals Evaluate the following iterated integrals. 6.0201(3x2+4y3)dydx Problem 7E: Iterated integrals Evaluate the following iterated integrals. 7.1302x2ydxdy Problem 8E: Iterated integrals Evaluate the following iterated integrals. 8.0321(2x+3y)dxdy Problem 9E: Iterated integrals Evaluate the following iterated integrals. 9.130/2xsinydydx Problem 10E: Iterated integrals Evaluate the following iterated integrals. 10.1312(y2+y)dxdy Problem 11E: Iterated integrals Evaluate the following iterated integrals. 11.1404uvdudv Problem 12E Problem 13E: Iterated integrals Evaluate the following iterated integrals. 13.0ln016xe3ydxdy Problem 14E: Iterated integrals Evaluate the following iterated integrals. 14.0101y1+x2dxdy Problem 15E: Iterated integrals Evaluate the following iterated integrals. 15.1ln50ln3ex+ydxdy Problem 16E: Iterated integrals Evaluate the following iterated integrals. 16.0/403rsecdrd Problem 17E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 18E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 19E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 20E Problem 21E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 22E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 23E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 24E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 25E: Double integrals Evaluate each double integral over the region R by converting it to an iterated... Problem 26E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 27E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 28E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 29E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 30E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 31E: Choose a convenient order When convened to an iterated integral, the following double integrals are... Problem 32E: Average value Compute the average value of the following functions over the region R.... Problem 33E: Average value Compute the average value of the following functions over the region R.... Problem 34E: Average value Compute the average value of the following functions over the region R.... Problem 35E: Average value 35.Find the average squared distance between the points of R={(x,y):2x2,0y2} and the... Problem 36E: Average value 35.Find the average squared distance between the points of R={(x,y):0x3,0y3} and the... Problem 37E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 38E: Symmetry Evaluate the following integrals using symmetry arguments. Let R={(x,y):=axa,byb}, where a... Problem 39E: Computing populations The population densities in nine districts of a rectangular county are shown... Problem 40E Problem 41E: Pictures of solids Draw the solid whose volume is given by the following iterated integrals. Then... Problem 42E Problem 43E: More integration practice Evaluate the following iterated integrals. 43.1212xx+ydydx Problem 44E: More integration practice Evaluate the following iterated integrals. 44.0201x5y2ex3y3dydx Problem 45E: More integration practice Evaluate the following iterated integrals. 45.01143yx+y2dxdy Problem 46E: More integration practice Evaluate the following iterated integrals. 46.1402eyxdydx Problem 47E: Volumes of solids Find the volume of the following solids. 47.The solid beneath the cylinder... Problem 48E Problem 49E: Volumes of solids Find the volume of the following solids. 49.The solid beneath the cylinder... Problem 50E Problem 51E: Solving for a parameter Let R={x,y}:{0x,0ya}. For what values of a, with 0a, is Rsin(x+y)dA equal to... Problem 52E Problem 53E: Zero average value Find the value of a 0 such that the average value of the following functions... Problem 54E Problem 55E: Density and mass Suppose a thin rectangular plate, represented by a region R in the xy-plane, has a... Problem 56E: Approximating volume Propose a method based on Riemann sums to approximate the volume of the shed... Problem 57E: Cylinders Let S be the solid in 3between the cylinder z = f(x) and the region, where f(x) 0 on R.... Problem 58E: Product of integrals Suppose f(x, y) = g(x)h(y), where g and h are continuous functions for all real... Problem 59E Problem 60E Problem 61E: A generalization Let R be as in Exercise 60, let F be an antiderivative of f with F(0) = 0, and let... format_list_bulleted