1 Functions And Limits 2 Derivatives 3 Applications Of Differentiation 4 Integrals 5 Applications Of Integration 6 Inverse Functions 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Infinite Sequences And Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus 17 Second-order Differential Equations expand_more
15.1 Double Integrals Over Rectangles 15.2 Double Integrals Over General Regions 15.3 Double Integrals In Polar Coordinates 15.4 Applications Of Double Integrals 15.5 Surface Area 15.6 Triple Integrals 15.7 Triple Integrals In Cylindrical Coordinates 15.8 Triple Integrals In Spherical Coordinates 15.9 Change Of Variables In Multiple Integrals 15.R Review 15.P Problem Plus expand_more
Problem 1E: 16 Evaluate the iterated integral. 150x(8x2y)dydx Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: 16 Evaluate the iterated integral. 010ev1+evdwdv Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E: Draw an example of a region that is atype I but not type II btype II but not type I Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E: 1516 Set up iterated integrals for both orders of integration. Then evaluate the double integral... Problem 17E Problem 18E: 1722 Evaluate the double integral. D(x2+2y)dA, D is bounded by y=x,y=x3,x0 Problem 19E: 1722 Evaluate the double integral. Dy2dA, D is triangular region with vertices (0,1),(1,2),(4,1) Problem 20E: 1722 Evaluate the double integral. DxydA, D is enclosed by the quarter-circle y=1x2,x0, and the axes Problem 21E: 1722 Evaluate the double integral. D(2xy)dA, D is bounded by the circle with center the origin and... Problem 22E: 1722 Evaluate the double integral. DydA, D is triangular region with vertices (0,0),(1,1),(4,0), and... Problem 23E: 2332 Find the volume of the given solid. Under the plane 3x+2yz=0 and above the region enclosed by... Problem 24E Problem 25E: 2332 Find the volume of the given solid. Under the surface z=xy and above the triangle with vertices... Problem 26E: 2332 Find the volume of the given solid. Enclosed by the paraboloid z=x2+y2+1 and the planes... Problem 27E Problem 28E: 2332 Find the volume of the given solid. Bounded by the planes z=x,y=x,x+y=2, and z=0 Problem 29E Problem 30E: 2332 Find the volume of the given solid. Bounded by the cylinders y2+z2=4 and the planes... Problem 31E Problem 32E: 2332 Find the volume of the given solid. Bounded by the cylinders x2+y2=r2 and y2+z2=r2 Problem 33E Problem 34E Problem 35E Problem 36E: 3538 Find the volume of the solid by subtracting two volumes. The solid enclosed by the parabolic... Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E: 4144 Use a computer algebra system to find the exact volume of the solid. Between the paraboloids... Problem 43E: 4144 Use a computer algebra system to find the exact volume of the solid. Enclosed by z=1x2y2 and... Problem 44E Problem 45E Problem 46E: 4550 Sketch the region of integration and change the order of integration. 02x24f(x,y)dydx Problem 47E: 4550 Sketch the region of integration and change the order of integration. 0/20cosxf(x,y)dydx Problem 48E: 4550 Sketch the region of integration and change the order of integration. 2204y2f(x,y)dxdy Problem 49E Problem 50E: 4550 Sketch the region of integration and change the order of integration. 01arctanx/4f(x,y)dydx Problem 51E: 5156 Evaluate the integral by reversing the order of integration. 013y3ex2dxdy Problem 52E: 5156 Evaluate the integral by reversing the order of integration. 01x21ysinydydx Problem 53E: 5156 Evaluate the integral by reversing the order of integration. 01x1y3+1dydx Problem 54E Problem 55E: 5156 Evaluate the integral by reversing the order of integration. 01arctany/2cosx1+cos2xdxdy Problem 56E Problem 57E: 5758 Express D as a union of regions of type I and type II and evaluate the integral. Dx2dA Problem 58E Problem 59E: 5960 Use Property 11 to estimate the value of the integral. s4x2y2dA,S={(x,y)|x2+y21,x0} Problem 60E Problem 61E: 6162 Find the average value of f over the region D. f(x,y)=xy,D is the triangle with vertices... Problem 62E Problem 63E Problem 64E: In evaluating a double integral over a region D, a sum of iterated integrals was obtained as... Problem 65E: 6569 Use geometry or symmetry, or both, to evaluate the double integral. D(x+2)dA, D={(x,y)|0y9x2} Problem 66E: 6569 Use geometry or symmetry, or both, to evaluate the double integral. DR2x2y2dA, D is the disk... Problem 67E Problem 68E Problem 69E Problem 70E: Graph the solid bounded by the plane x+y+z=1 and the paraboloid z=4x2y2 and find its exact volume.... format_list_bulleted