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Math
Calculus
Calculus: Early Transcendentals
Chapter 16.2, Problem 31E
Chapter 16.2, Problem 31E
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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16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem For Line Integrals
16.4 Green's Theorem
16.5 Curl And Divergence
16.6 Parametric Surfaces And Their Areas
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem
16.10 Summary
Chapter Questions
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Problem 1E: Evaluate the line integral, where C is the given curve. 1. C y ds, C: x = t2, y = 2t, 0 t 3
Problem 2E: Evaluate the line integral, where C is the given curve. 2. C (x/y) ds, C: x = t3, y = t4, 1 t 2
Problem 3E: Evaluate the line integral, where C is the given curve. 3. C xy4 ds, C is the right half of the...
Problem 4E: Evaluate the line integral, where C is the given curve. 4. C xey ds, C is the line segment from (2,...
Problem 5E: Evaluate the line integral, where C is the given curve. 5. C (x2y + sin x) dy, C is the arc of the...
Problem 6E: Evaluate the line integral, where C is the given curve. 6. C ex dx, C is the arc of the curve x = y3...
Problem 7E: Evaluate the line integral, where C is the given plane curve. 7. C(x+2y)dx+x2dy
Problem 8E
Problem 9E: Evaluate the line integral, where C is the given space curve. 9. Cx2yds, C:x=cost,y=sint,z=t,0t/2
Problem 10E: Evaluate the line integral, where C is the given space curve. 10. Cy2zds C is the line segment from...
Problem 11E: Evaluate the line integral, where C is the given space curve. 11. Cxeyzds C is the line segment from...
Problem 12E: Evaluate the line integral, where C is the given space curve. 12....
Problem 13E: Evaluate the line integral, where C is the given space curve. 13. Cxyeyzdy,C:x=t,y=t2,z=t3,0t1
Problem 14E: Evaluate the line integral, where C is the given space curve. 14....
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E: Let F be the vector field shown in the figure. (a) If C1 is the vertical line segment from (3, 3) to...
Problem 20E: The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1, and...
Problem 21E
Problem 22E
Problem 23E: Evaluate the line integral C F dr, where C is given by the vector function r(t). 21. F(x, y, z) =...
Problem 24E: Evaluate the line integral C F dr, where C is given by the vector function r(t). 22. F(x, y, z) = x...
Problem 25E: Use a calculator or computer to evaluate the line integral correct to four decimal places. 25. CFdr...
Problem 26E
Problem 27E
Problem 28E: Use a calculator or computer to evaluate the line integral correct to four decimal places. 28....
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E: A thin wire is bent into the shape of a semicircle x2 + y2 = 4, x 0. If the linear density is a...
Problem 36E: A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius...
Problem 37E
Problem 38E
Problem 39E: If a wire with linear density (x, y) lies along a plane curve C, its moments of inertia about the x-...
Problem 40E: If a wire with linear density (x, y, z) lies along a space curve C, its moments of inertia about the...
Problem 41E: Find the work done by the force field F(x, y) = x i + (y + 2) j in moving an object along an arch of...
Problem 42E: Find the work done by the force field F(x, y) = x2 i + yex j on a particle that moves along the...
Problem 43E: Find the work done by the force field F(x, y, z) = x y2, y z2, z x2 on a particle that moves along...
Problem 44E: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)...
Problem 45E: The position of an object with mass m at time t is r(t) = at2 i + bt3j, 0 t 1. (a) What is the...
Problem 46E
Problem 47E: A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with a radius...
Problem 48E
Problem 49E: (a) Show that a constant force field does zero work on a particle that moves once uniformly around...
Problem 50E
Problem 51E
Problem 52E
Problem 53E: An object moves along the curve C shown in the figure from (1, 2) to (9, 8). The lengths of the...
Problem 54E: Experiments show that a steady current I in a long wire produces a magnetic field B that is tangent...
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