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Math
Calculus
Calculus: Early Transcendentals
Chapter 15.2, Problem 80E
Chapter 15.2, Problem 80E
BUY
Calculus: Early Transcendentals
9th Edition
ISBN:
9780357631478
Author: James Stewart, Daniel K. Clegg, Saleem Watson
Publisher:
Cengage Learning
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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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
Chapter Questions
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Problem 1E: Evaluate the iterated integral. 1. 1s0x(8x2y)dydx
Problem 2E: Evaluate the iterated integral. 2. 020y2x2ydxdy
Problem 3E: Evaluate the iterated integral. 3. 010yxey3dxdy
Problem 4E: Evaluate the iterated integral. 4. 0/20xxsinydydx
Problem 5E: Evaluate the iterated integral. 5. 010s2cos(s3)dtds
Problem 6E: Evaluate the iterated integral. 6. 010ex1+exdwdv
Problem 7E: (a) Express the double integral Df(x,y)dA as an iterated integral for the given function f and...
Problem 8E: (a) Express the double integral Df(x,y)dA as an iterated integral for the given function f and...
Problem 9E: (a) Express the double integral Df(x,y)dA as an iterated integral for the given function f and...
Problem 10E: (a) Express the double integral Df(x,y)dA as an iterated integral for the given function f and...
Problem 11E: Evaluate the double integral. 7. Dyx2+1dA,D={(x,y)|0x4,0yx}
Problem 12E: Evaluate the double integral. 8. D(2x+y)dA,D={(x,y)|1y2,y1x1}
Problem 13E: Evaluate the double integral. 9. Dey2dA,D={(x,y)|0y3,0xy}
Problem 14E: Evaluate the double integral. 10. Dyx2y2dA,D={(x,y)|0x2,0yx}
Problem 15E: Draw an example of a region that is (a) type I but not type II (b) type II but not type I
Problem 16E: Draw an example of a region that is (a) both type I and type II (b) neither type I nor type II
Problem 17E: Express D as a region of type I and also as a region of type II. Then evaluate the double integral...
Problem 18E: Express D as a region of type I and also as a region of type II. Then evaluate the double integral...
Problem 19E: Set up iterated integrals for both orders of integration. Then evaluate the double integral using...
Problem 20E: Set up iterated integrals for both orders of integration. Then evaluate the double integral using...
Problem 21E: Set up iterated integrals for both orders of integration. Then evaluate the double integral using...
Problem 22E: Set up iterated integrals for both orders of integration. Then evaluate the double integral using...
Problem 23E: Evaluate the double integral. 17.DxcosydA, D is bounded by y = 0. y = x2, x = 1
Problem 24E: Evaluate the double integral. 18. D(x2+2y)dA, D is bounded by y = x, y = x3, x 0
Problem 25E: Evaluate the double integral. 19. Dy2dA, D is the triangular region with vertices (0, 1), (1, 2),...
Problem 26E: Evaluate the double integral. 20. DxydA, D is enclosed by the quarter-circle y=1x2,x0, and the axes
Problem 27E: Evaluate the double integral. 21. D(2xy)dA, D is bounded by the circle with center the origin and...
Problem 28E: Evaluate the double integral. 22. DydA, D is the triangular region with vertices (0, 0), (1, 1), and...
Problem 29E: The figure shows a surface and a region D in the x y-plane. (a) Set up an iterated double integral...
Problem 30E: The figure shows a surface and a region D in the x y-plane. (a) Set up an iterated double integral...
Problem 31E: Find the volume of the given solid. 23. Under the plane 3x + 2y z = 0 and above the region enclosed...
Problem 32E: Find the volume of the given solid. 24. Under the surface z = 1+ x2y2 and above the region enclosed...
Problem 33E: Find the volume of the given solid. 25. Under the surface z = xy and above the triangle with...
Problem 34E: Find the volume of the given solid. 26. Enclosed by the paraboloid z = x2 + y2 + 1 and the planes x...
Problem 35E: Find the volume of the given solid. 27. The tetrahedron enclosed by the coordinate planes and the...
Problem 36E: Find the volume of the given solid. 28. Bounded by the planes z = x, y = x, x + y = 2, and z = 0
Problem 37E: Find the volume of the given solid. 29. Enclosed by the cylinders z = x2, y = x2 and the planes z =...
Problem 38E: Find the volume of the given solid. 30. Bounded by the cylinder y2 + z2 = 4 and the planes x = 2y, x...
Problem 39E: Find the volume of the given solid. 31. Bounded by the cylinder x2 + y2 = 1 and the planes y = z, x...
Problem 40E: Find the volume of the given solid. 32. Bounded by the cylinders x2 + y2 = r2 and y2 + z2 = r2
Problem 41E: Use a graphing calculator or computer to estimate the x-coordinates of the points of intersection of...
Problem 42E: Find the approximate volume of the solid in the first octant that is bounded by the planes y=x,z=0 ,...
Problem 43E: Find the volume of the solid by subtracting two volumes. 35. The solid enclosed by the parabolic...
Problem 44E: Find the volume of the solid by subtracting two volumes. 36. The solid enclosed by the parabolic...
Problem 45E: Find the volume of the solid by subtracting two volumes. 37. The solid under the plane z = 3, above...
Problem 46E: Find the volume of the solid by subtracting two volumes. 38. The solid in the first octant under the...
Problem 47E: Sketch the solid whose volume is given by the iterated integral. 0101x(1xy)dydx
Problem 48E: Sketch the solid whose volume is given by the iterated integral. 0101x2(1x)dydx
Problem 49E
Problem 50E
Problem 51E: Use a computer algebra system to find the exact volume of the solid. 51. Under the surface...
Problem 52E: Use a computer algebra system to find the exact volume of the solid. 52. Between the paraboloids...
Problem 53E: Use a computer algebra system to find the exact volume of the solid. 53. Enclosed by z=1x2y2 and z=0
Problem 54E: Use a computer algebra system to find the exact volume of the solid. 54. Enclosed by z=x2+y2 and...
Problem 55E: Sketch the region of integration and change the order of integration. 010yf(x,y)dxdy
Problem 56E: Sketch the region of integration and change the order of integration. 02x24f(x,y)dydx
Problem 57E: Sketch the region of integration and change the order of integration. 0/20cosxf(x,y)dydx
Problem 58E: Sketch the region of integration and change the order of integration. 2204y2f(x,y)dxdy
Problem 59E: Sketch the region of integration and change the order of integration. 120lnxf(x,y)dydx
Problem 60E: Sketch the region of integration and change the order of integration. 01arctanx/4f(x,y)dydx
Problem 61E: Evaluate the integral by reversing the order of integration. 013y3ex2dxdy
Problem 62E: Evaluate the integral by reversing the order of integration. 01x21ysinydydx
Problem 63E: Evaluate the integral by reversing the order of integration. 01x1y3+1dydx
Problem 64E: Evaluate the integral by reversing the order of integration. 02y/21ycos(x31)dxdy
Problem 65E: Evaluate the integral by reversing the order of integration. 01arcsiny/2cosx1+cos2xdxdy
Problem 66E: Evaluate the integral by reversing the order of integration. 08y32ex4dxdy
Problem 67E: Express D as a union of regions of type I or type II and evaluate the integral. 57. Dx2dA
Problem 68E: Express D as a union of regions of type I or type II and evaluate the integral. 58. DydA
Problem 69E
Problem 70E: Use Property 10 to estimate the value of the integral. 70. Tsin4(x+y)dA,T is the triangle enclosed...
Problem 71E: Find the averge value of f over the region D. 61. f(x, y) = xy, D is the triangle with vertices (0,...
Problem 72E: Find the averge value of f over the region D. 62. f(x, y) = x sin y, D is enclosed by the curves y =...
Problem 73E
Problem 74E: In evaluating a double integral over a region D, a sum of iterated integrals was obtained as...
Problem 75E: Use geometry or symmetry, or both, to evaluate the double integral. 65. D(x+2)dA, D=(x,y)0y9x2
Problem 76E: Use geometry or symmetry, or both, to evaluate the double integral. 66. DR2x2y2dA, D is the disk...
Problem 77E: Use geometry or symmetry, or both, to evaluate the double integral. 67. D(2x+3y)dA, D is the...
Problem 78E: Use geometry or symmetry, or both, to evaluate the double integral. 68. D(2+x2y3y2sinx)dA,...
Problem 79E: Use geometry or symmetry, or both, to evaluate the double integral. 69. D(ax3+by3+a2x2)dA,...
Problem 80E
Problem 81E
Problem 82E
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