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Math
Calculus
Calculus, Early Transcendentals
Chapter 15.6, Problem 5DP
Chapter 15.6, Problem 5DP
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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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 integral in Example 1, integrating first with respect to y, then z, and then x. EXAMPLE...
Problem 2E: Evaluate the integral E(xy+z2)dv, where E=(x,y,z)0x2,0y1,0z3 using three different orders of...
Problem 3E: Evaluate the iterated integral. 3.020z20yz(2xy)dxdydz
Problem 4E: Evaluate the iterated integral. 4.01y2y0x+y6xydzdxdy
Problem 5E: Evaluate the iterated integral. 5. 1202z0lnxxeydydxdz
Problem 6E
Problem 7E: Evaluate the iterated integral. 7. 1312yzzydxdzdy
Problem 8E: Evaluate the iterated integral. 8. 010102x2y2xyezdzdydx
Problem 9E: (a) Express the triple integral Ef(x,y,z)dV as an iterated integral for the given function f and...
Problem 10E: (a) Express the triple integral Ef(x,y,z)dV as an iterated integral for the given function f and...
Problem 11E: (a) Express the triple integral Ef(x,y,z)dV as an iterated integral for the given function f and...
Problem 12E: (a) Express the triple integral Ef(x,y,z)dV as an iterated integral for the given function f and...
Problem 13E: Evaluate the triple integral. 9. EydV, where E=(x,y,z)0x3,0yx,xyzx+y
Problem 14E: Evaluate the triple integral. 10.EezydV, where E=(x,y,z)0y1,yx1,0zxy
Problem 15E: Evaluate the triple integral. 15. E1/x3dV , where E=(x,y,z)0y1,0zy2,1xz+1
Problem 16E: Evaluate the triple integral. 12. EsinydV, where E lies below the plane z = x and above the...
Problem 17E: Evaluate the triple integral. 13. E6xydV, where E lies under the plane z = 1 + x + y and above the...
Problem 18E: Evaluate the triple integral. 14. E(xy)dV, where E lies enclosed by the surface z = x2 1, z = 1 ...
Problem 19E: Evaluate the triple integral. 15. Ty2dV. where T is the solid tetrahedron with vertices (0, 0,0),...
Problem 20E: Evaluate the triple integral. 16. TxzdV, where T is the solid tetrahedron with vertices (0, 0, 0),...
Problem 21E: Evaluate the triple integral. 17. ExdV, where E is bounded by the paraboloid x 4y2 + 4z2 and the...
Problem 22E: Evaluate the triple integral. 18. EzdV, where E is bounded by the cylinder y2 + z2 = 9 and the...
Problem 23E: Use a triple integral to find the volume of the given solid. 19. The tetrahedron enclosed by the...
Problem 24E: Use a triple integral to find the volume of the given solid. 20. The solid enclosed by the...
Problem 25E: Use a triple integral to find the volume of the given solid. 21. The solid enclosed by the cylinder...
Problem 26E: Use a triple integral to find the volume of the given solid. 22. The solid enclosed by the cylinder...
Problem 27E: Use the Midpoint Rule for triple integrals (Exercise 24) to estimate the value of the integral....
Problem 28E: Midpoint Rule for Triple Integrals In the Midpoint Rule for triple integrals we use a triple Riemann...
Problem 29E: Midpoint Rule for Triple Integrals In the Midpoint Rule for triple integrals we use a triple Riemann...
Problem 30E
Problem 31E: Express the integralEf(x,y,z)dV, as an iterated integral in six different ways, where E is the solid...
Problem 32E: Express the integral Ef(x,y,z)dV, as an iterated integral in six different ways, where E is the...
Problem 33E: Express the integral Ef(x,y,z)dV,as an iterated integral in six different ways, where E is the solid...
Problem 34E: Express the integral Ef(x,y,z)dV,as an iterated integral in six different ways, where E is the solid...
Problem 35E: The figure shows the region of integration for the integral 01x101yf(x,y,z)dzdydx Rewrite this...
Problem 36E: The figure shows the region of integration for the integral 0101x201xf(x,y,z)dydzdx Rewrite this...
Problem 37E: Write five other iterated integrals that are equal to the given iterated integral. 35....
Problem 38E: Write five other iterated integrals that are equal to the given iterated integral. 36....
Problem 39E: Evaluate the triple integral using only geometric interpretation and symmetry. 37.c(4+5x2yz2)dV,...
Problem 40E: Evaluate the triple integral using only geometric interpretation and symmetry. 38. B(z3+siny+3)dV,...
Problem 41E: Find the mass and center of mass of the solid E with the given density function . 39. E lies above...
Problem 42E: Find the mass and center of mass of the solid R with the given density function . 40. E is bounded...
Problem 43E: Find the mass and center of mass of the solid E with the given density function . 41. E. is the cube...
Problem 44E: Find the mass and center of mass of the solid F. with the given density function . 42. E is the...
Problem 45E: Assume that the solid has constant density k. 43. Find the moments of inertia for a cube with side...
Problem 46E: Assume that the solid has constant density k. 44. Find the moments of inertia for a rectangular...
Problem 47E
Problem 48E: Assume that the solid has constant density k. 46. Find the moment of inertia about the z-axis of the...
Problem 49E
Problem 50E: Set up, but do not evaluate, integral expressions for (a) the mass, (b) the center of mass, and (c)...
Problem 51E
Problem 52E
Problem 53E
Problem 54E: If E is the solid of Exercise 22 with density function (x,y,z)=x2+y2 , find the following...
Problem 55E: The average value of a function f (x, y, z) over a solid region E is defined to be...
Problem 56E: The average value of a function f (x, y, z) over a solid region E is defined to be...
Problem 57E
Problem 58E: Find the average height of the points in the solid hemisphere x2+y2+z21,z0.
Problem 59E
Problem 1DP
Problem 2DP
Problem 3DP
Problem 4DP
Problem 5DP
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A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
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