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 1RE: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 2RE: Evaluating integrals Evaluate the following integrals as they are written. 2.1214xy(x2+y2)2dxdy Problem 3RE: Evaluating integrals Evaluate the following integrals as they are written. 3.131e1xydydx Problem 4RE: Evaluating integrals Evaluate the following integrals as they are written. 4.120lnxx3eydydx Problem 5RE: Changing the order of integration Assuming f is integrable, change the order of integration in the... Problem 6RE: Changing the order of integration Assuming f is integrable, change the order of integration in the... Problem 7RE: Changing the order of integration Assuming f is integrable, change the order of integration in the... Problem 8RE: Area of plane regions Use double integrals to compute the area of the following regions. Make a... Problem 9RE: Area of plane regions Use double integrals to compute the area of the following regions. Make a... Problem 10RE: Area of plane regions Use double integrals to compute the area of the following regions. Make a... Problem 11RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 12RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 13RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 14RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 15RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 16RE: Miscellaneous double integrals Choose a convenient method for evaluating the following integrals.... Problem 17RE: Cartesian to polar coordinates Evaluate the following integrals over the specified region.... Problem 18RE: Cartesian to polar coordinates Evaluate the following integrals over the specified region.... Problem 19RE: Computing areas Sketch the following regions and use integration to find their areas. 19.The region... Problem 20RE: Computing areas Sketch the following regions and use integration to find their areas. 20.The region... Problem 21RE: Computing areas Sketch the following regions and use integration to find their areas. 21.The region... Problem 22RE: Average values 22.Find the average value of z=16x2y2 over the disk in the xy-plane centered at the... Problem 23RE: Average values 23.Find the average distance from the points in the solid cone bounded by z=2x2+y2 to... Problem 24RE Problem 25RE Problem 26RE: Changing order of integration Rewrite the following integrals using the indicated order of... Problem 27RE: Triple integrals Evaluate the following integrals, changing the order of integration if needed.... Problem 28RE: Triple integrals Evaluate the following integrals, changing the order of integration if needed.... Problem 29RE: Triple integrals Evaluate the following integrals, changing the order of integration if needed.... Problem 30RE: Triple integrals Evaluate the following integrals, changing the order of integration if needed.... Problem 31RE: Triple integrals Evaluate the following integrals, changing the order of integration if needed.... Problem 32RE: Volumes of solids Find the volume of the following solids. 32.The prism in the first octant bounded... Problem 33RE: Volumes of solids Find the volume of the following solids. 33.One of the wedges formed when the... Problem 34RE: Volumes of solids Find the volume of the following solids. 34.The solid bounded by the parabolic... Problem 35RE: Volumes of solids Find the volume of the following solids. 35.The solid common to the two cylinders... Problem 36RE: Volumes of solids Find the volume of the following solids. 36.The tetrahedron with vertices (0, 0,... Problem 37RE: Single to double integral Evaluate 01/2(sin12xsin1x)dx by converting it to a double integral. Problem 38RE: Tetrahedron limits Let D be the tetrahedron with vertices at (0,0,0), (1,0,0), (0, 2,0), and... Problem 39RE: A polynomial cube Let D = {(x, y, z): 0 x y2, 0 y z2, 0 z 2} a.Use a triple integral to find... Problem 40RE: Average value 40.Find the average of the square of the distance between the origin and the points in... Problem 41RE: Average value 41.Find the average x-coordinate of the points in the prism D = {(x, y, z): 0 x 1, 0... Problem 42RE: Integrals in cylindrical coordinates Evaluate the following integrals in cylindrical coordinates.... Problem 43RE: Integrals in cylindrical coordinates Evaluate the following integrals in cylindrical coordinates.... Problem 44RE: Volumes in cylindrical coordinates Use integration in cylindrical coordinates to find the volume of... Problem 45RE: Volumes in cylindrical coordinates Use integration in cylindrical coordinates to find the volume of... Problem 46RE: Integrals in spherical coordinates Evaluate the following integrals in spherical coordinates.... Problem 47RE: Integrals in spherical coordinates Evaluate the following integrals in spherical coordinates.... Problem 48RE: Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the... Problem 49RE: Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the... Problem 50RE: Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the... Problem 51RE: Center of mass of constant-density plates Find the center of mass (centroid) of the following thin... Problem 52RE: Center of mass of constant-density plates Find the center of mass (centroid) of the following thin... Problem 53RE: Center of mass of constant-density plates Find the center of mass (centroid) of the following thin... Problem 54RE: Center of mass of constant-density plates Find the center of mass (centroid) of the following thin... Problem 55RE: Center of mass of constant-density solids Find the center of mass of the following solids, assuming... Problem 56RE: Center of mass of constant-density solids Find the center of mass of the following solids, assuming... Problem 57RE Problem 58RE: Variable-density solids Find the coordinates of the center of mass of the following solids with the... Problem 59RE: Center of mass for general objects Consider the following two- and three-dimensional regions.... Problem 60RE Problem 61RE Problem 62RE Problem 63RE Problem 64RE: Volume and weight of a fish tank A spherical fish tank with a radius of 1 ft is filled with water to... Problem 65RE Problem 66RE: Transforming a square Let S = {(u, v): 0 u 1, 0 v 1} be a unit square in the uv-plane. Find the... Problem 67RE Problem 68RE: Transforming a square Let S = {(u, v): 0 u 1, 0 v 1} be a unit square in the uv-plane. Find the... Problem 69RE Problem 70RE: Computing Jacobians Compute the Jacobian J(u, v) of the following transformations. 70.T: x = u + v,... Problem 71RE Problem 72RE Problem 73RE: Double integralstransformation given To evaluate the following integrals, carry out the following... Problem 74RE: Double integralstransformation given To evaluate the following integrals, carry out the following... Problem 75RE: Double integralstransformation given To evaluate the following integrals, carry out the following... Problem 76RE: Double integralstransformation given To evaluate the following integrals, carry out the following... Problem 77RE: Double integrals Evaluate the following integrals using a change of variables. Sketch the original... Problem 78RE: Double integrals Evaluate the following integrals using a change of variables. Sketch the original... Problem 79RE: Triple integrals Use a change of variables to evaluate the following integrals. 79.DyzdV;D is... Problem 80RE: Triple integrals Use a change of variables to evaluate the following integrals. 80.DxdV; D is... format_list_bulleted
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