Calculus: Early Transcendentals, Enhanced Etext
Calculus: Early Transcendentals, Enhanced Etext
12th Edition
ISBN: 9781119777984
Author: Howard Anton; Irl C. Bivens; Stephen Davis
Publisher: Wiley Global Education US
bartleby

Videos

Textbook Question
Book Icon
Chapter 15.4, Problem 1QCE

If C is the square with vertices ± 1 ,   ± 1 oriented counter- clockwise, then

∫ C − y   d x + x   d y = ______

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 15.3, Problem 41ES
Next
Chapter 15.4, Problem 2QCE

Chapter 15 Solutions

Calculus: Early Transcendentals, Enhanced Etext

Ch. 15.1 - The function (x,y,z)=xy+yz+xz is a potential for...Ch. 15.1 - The vector field F(x,y,z)=, defined for...Ch. 15.1 - An inverse-square field is one that can be written...Ch. 15.1 - The vector field has divergence and curl Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Determine whether the statement about the vector...Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Determine whether the statement is true or false....
Ch. 15.1 - Determine whether the statement is true or false....Ch. 15.1 - Confirm that is a potential function for F(r) on...Ch. 15.1 - Find div F and curl F . F(x,y,z)=x2i2j+yzkCh. 15.1 - Find div F and curl F . F(x,y,z)=xz3i+2y4x2j+5z2ykCh. 15.1 - Find div and curl . Ch. 15.1 - Find div and curl . Ch. 15.1 - Prob. 21ESCh. 15.1 - Find div F and curl F ....Ch. 15.1 - Find(FG).F(x,y,z)=2xi+j+4ykG(x,y,z)=xi+yjzkCh. 15.1 - Find(F).F(x,y,z)=sinxi+cos(xy)j+zkCh. 15.1 - Find(F).F(x,y,z)=exzi+3xeyjeyzkCh. 15.1 - Find(F).F(x,y,z)=xyj+xyzkCh. 15.1 - Use a CAS to check the calculations in Exercises...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Rewrite the identities in Exercises 31, 33, 35,...Ch. 15.1 - Rewrite the identities in Exercises 32, 34, 36,...Ch. 15.1 - Verify that the radius vector r=xi+yj+zk has the...Ch. 15.1 - Verify that the radius vector r=xi+yj+zk has the...Ch. 15.1 - Letr=xi+yj+zk,letr=r,letf be a differentiable...Ch. 15.1 - (a) Use part (a) of Exercise 43, Exercise 36, and...Ch. 15.1 - Use the result in Exercise 43(b) to show that the...Ch. 15.1 - Use the result of Exercise 43(b) to show that if F...Ch. 15.1 - A curve C is called a flow line of a vector field...Ch. 15.1 - Find a differential equation satisfied by the flow...Ch. 15.1 - Find a differential equation satisfied by the flow...Ch. 15.1 - Prob. 51ESCh. 15.2 - The area of the surface extending upward from the...Ch. 15.2 - Suppose that a wire has equation y=1x(0x1) and...Ch. 15.2 - If C is the curve represented by the equations...Ch. 15.2 - Prob. 4QCECh. 15.2 - Let C be the line segment from (0.0)to(0,1). In...Ch. 15.2 - Let C be the line segment from (0,2)to(0,4). ln...Ch. 15.2 - Evaluate CFdr by inspection for the force field...Ch. 15.2 - Evaluate CFdr by inspection for the force field...Ch. 15.2 - Use (30) to explain why the line integral in part...Ch. 15.2 - (a) Use (30) to explain why the line integral in...Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Prob. 8ESCh. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Let C be the curve represented by the equations...Ch. 15.2 - Let C be the curve represented by the equations...Ch. 15.2 - In each part, evaluate the integral...Ch. 15.2 - In each part, evaluate the integral Cydx+zdyxdz...Ch. 15.2 - Prob. 15ESCh. 15.2 - Determine whether the statement is true or false....Ch. 15.2 - If a smooth oriented curve C in the xy-plane is a...Ch. 15.2 - Evaluate the line integral with respect to s along...Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Use a CAS to evaluate the line integrals along the...Ch. 15.2 - Use a CAS to evaluate the line integrals along the...Ch. 15.2 - Evaluate Cydxxdy along the curve C shown in the...Ch. 15.2 - Evaluate Cydxxdy along the curve C shown in the...Ch. 15.2 - Evaluate Cx2zdxyx2dy+3dz along the curve C shown...Ch. 15.2 - Evaluate Cx2zdxyx2dy+3dz along the curve C shown...Ch. 15.2 - Evaluate CFdr along the curve C....Ch. 15.2 - Evaluate CFdr along the curves C....Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force field...Ch. 15.2 - Find the work done by the force field...Ch. 15.2 - Use a line integral to find the area of the...Ch. 15.2 - Use a line integral to find the area of the...Ch. 15.2 - As illustrated in the accompanying figure, a...Ch. 15.2 - Evaluate the integral Cxdyydxx2+y2, where C is the...Ch. 15.2 - Suppose that a particle moves through the force...Ch. 15.2 - A farmer weighting 150 lb carries a sack of gain...Ch. 15.2 - Suppose that a curve C in the xy-plane is smoothly...Ch. 15.3 - If C is a piecewise smooth curve from...Ch. 15.3 - Prob. 2QCECh. 15.3 - A potential function for the vector field...Ch. 15.3 - If a, b. and c are nonzero real numbers such that...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - In each part, evaluate C2xy3dx+1+3x2y2dy over the...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Prob. 22ESCh. 15.3 - Find the exact value of CFdr using any method....Ch. 15.3 - Use the numerical integration capability of a CAS...Ch. 15.3 - Is the vector field conservative? Explain.Ch. 15.3 - Is the vector field conservative? Explain.Ch. 15.3 - Prob. 30ESCh. 15.3 - Prove: If Fx,y,z=fx,y,zi+gx,y,zj+hx,y,zk is a...Ch. 15.3 - Find a nonzero function h for which...Ch. 15.3 - (a) In Example 3 of Section 15.1 we showed that...Ch. 15.3 - Use the result in Exercise 34(b). In each part,...Ch. 15.3 - Use the result in Exercise 34(b). Let...Ch. 15.3 - Prove Theorem 15.3.1 if C is a piecewise smooth...Ch. 15.3 - Prove that (b) implies (c) in Theorem 15.3.2.Ch. 15.3 - Complete the proof of Theorem 15.3.2 by showing...Ch. 15.4 - If C is the square with vertices 1,1 oriented...Ch. 15.4 - If C is the triangle with vertices 0,0,1,0,and1,1...Ch. 15.4 - Prob. 3QCECh. 15.4 - What region R and choice of functions fx,yandgx,y...Ch. 15.4 - Evaluate the line integral using Green’s Theorem...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Determine whether the statement is true or false....Ch. 15.4 - Use a CAS to check Green’s Theorem by evaluating...Ch. 15.4 - In Example 3, we used Green’s Theorem to obtain...Ch. 15.4 - Use a line integral to find the area of the region...Ch. 15.4 - Use a line integral to find the area of the...Ch. 15.4 - Use the formula A=12Cydx+xdy to find the area of...Ch. 15.4 - Use the formula A=12Cydx+xdy to find the area of...Ch. 15.4 - Suppose that Fx,y=fx,yi+gx,yj is a vector field...Ch. 15.4 - Suppose that Fx,y,=fx,yi+gx,yj is a vector field...Ch. 15.4 - Prob. 27ESCh. 15.4 - In the accompanying figure, C is a smooth oriented...Ch. 15.4 - Use Green’s Theorem to find the work done by the...Ch. 15.4 - Evaluate Cydxxdy, where C is cardioid r=a1+cos02Ch. 15.4 - Let R be a plane region with area A whose boundary...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Find a simple closed curve C with counterclockwise...Ch. 15.4 - (a) Let C be the line segment from a point a,b to...Ch. 15.4 - Evaluate the integral CFdr, where C is the...Ch. 15.4 - Evaluate the integral CFdr, where C is the...Ch. 15.4 - Discuss the role of the Fundamental Theorem of...Ch. 15.5 - Consider the surface integral fx,y,zdS. (a) If is...Ch. 15.5 - If is the triangular region with vertices...Ch. 15.5 - If is the sphere of radius 2 centered at the...Ch. 15.5 - If fx,y,z is the mass density function of a curved...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=x2;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=xy;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=x2y;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=xyz;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS...Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Sometimes evaluating a surface integral results in...Ch. 15.5 - Sometimes evaluating a surface integral results in...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - Set up, but do not evaluate, an iterated integral...Ch. 15.5 - Set up, but do not evaluate, an iterated integral...Ch. 15.5 - Use a CAS to confirm that the three integrals you...Ch. 15.5 - Try to confirm with a CAS that the three integrals...Ch. 15.5 - Set up, but do not evaluate, two different...Ch. 15.5 - Use a CAS to confirm that the two integrals you...Ch. 15.5 - Find the mass of the lamina with constant density...Ch. 15.5 - Find the mass of the lamina with constant density...Ch. 15.5 - Find the mass of the lamina that is the portion of...Ch. 15.5 - The centroid of a surface is defined by...Ch. 15.5 - The centroid of a surface is defined by...Ch. 15.5 - Evaluate the integral fx,y,zdS over the surface ...Ch. 15.5 - Prob. 37ESCh. 15.5 - Use a CAS to approximate the mass of the curved...Ch. 15.5 - The surface shown in the accompanying figure on...Ch. 15.5 - Discuss the similarities and differences between...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - Suppose that the surface of the unit cube in the...Ch. 15.6 - Find the flux of the constant vector field...Ch. 15.6 - Find the flux of F(x,y,z)=xi through a square of...Ch. 15.6 - Find the flux of F(x,y,z)=(y+1)j through a square...Ch. 15.6 - Find the flux of Fx,y,z=xi+yj+z2+4k through a 23...Ch. 15.6 - Find the flux of F(x,y,z)=2i+3j through a disk of...Ch. 15.6 - Find the flux of F(x,y,z)=9j+8k through a disk of...Ch. 15.6 - Prob. 8ESCh. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Let be the surface of the cube bounded by the...Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Find the flux of F across the surface by...Ch. 15.6 - Find the flux of F across the surface by...Ch. 15.6 - Let x,y,andz be measured in meters, and suppose...Ch. 15.6 - (a) Derive the analogs of Formulas (12) and (13)...Ch. 15.6 - (a) Derive the analogs of Formulas (12) and (13)...Ch. 15.6 - Let F=rkr,wherer=xi+yj+zkandkisaconstant. (Note...Ch. 15.6 - Discuss the similarities and differences between...Ch. 15.6 - Write a paragraph explaining the concept of flux...Ch. 15.7 - Let G be a solid whose surface is oriented outward...Ch. 15.7 - The outward flux of Fx,y,z=xi+yj+zk across any...Ch. 15.7 - If Fx,y,z is the velocity vector field for a...Ch. 15.7 - If F(r)=cr3r is an inverse-square field, and if ...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Prove that if r=xi+yj+zkand is the surface of a...Ch. 15.7 - Let Fx,y,z=ai+bj+ck be a constant vector field and...Ch. 15.7 - Find a vector field Fx,y,z that has (a) positive...Ch. 15.7 - Let Fx,y,z be a nonzero vector field in 3-space...Ch. 15.7 - Does the result in Exercise 25 remain true if the...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Use the Divergence Theorem to find all positive...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Let be the surface of the solid G that is...Ch. 15.8 - Let be a piecewise smooth oriented surface that...Ch. 15.8 - We showed in Example 2 that the vector field...Ch. 15.8 - (a) If 1and2 are two oriented surface that have...Ch. 15.8 - For steady-state flow, the maximum circulation...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Consider the vector field given by the formula...Ch. 15.8 - (a) Let denote the surface of a solid G with n...Ch. 15.8 - The figures in these exercises show a horizontal...Ch. 15.8 - The figures in these exercises show a horizontal...Ch. 15.8 - Let F(x,y,z) be a conservation vector field in...Ch. 15.8 - In 1831 the physicist Michael Faraday discovered...Ch. 15.8 - Discuss what it mean to say that the curl of a...Ch. 15.8 - Compare and contrast the Fundamental Theorem of...Ch. 15 - In words, what is a vector field? Give some...Ch. 15 - (a) Give a physical example of an inverse-square...Ch. 15 - Find an explicit coordinate expression for the...Ch. 15 - Find x+yxy.Ch. 15 - Find curl zi+xj+yk.Ch. 15 - Let Fx,y,z=xx2+y2i+yx2+y2j+zx2+y2k Sketch the...Ch. 15 - Assume that C is the parametric curve x=xt,y=yt,...Ch. 15 - (a) Express the mass M of a thin wire in 3-space...Ch. 15 - Give a physical interpretation of CFTds.Ch. 15 - State some alternative notations for CFTds.Ch. 15 - Evaluate the line integral. Cxyds;C:x2+y2=1Ch. 15 - Evaluate the line integral....Ch. 15 - State the Fundamental Theorem of Line Integrals,...Ch. 15 - Let Fx,y=yi2xj. (a) Find a nonzero function hx...Ch. 15 - Let Fx,y=yexy1i+xexyj. (a) Show that F is a...Ch. 15 - State Green's Theorem, including all of the...Ch. 15 - Express the area of a plane region as a line...Ch. 15 - Let and denote angles that satisfy 02 and assume...Ch. 15 - (a) Use Green's Theorem to prove that Cfxdx+gydy=0...Ch. 15 - Assume that is the parametric surface...Ch. 15 - Do you think that the surface in the accompanying...Ch. 15 - Give a physical interpretation of FndS.Ch. 15 - Find the flux of Fx,y,z=xi+yj+2zk through the...Ch. 15 - State the Divergence Theorem and Stokes' Theorem,...Ch. 15 - Let G be a solid with the surface oriented by...Ch. 15 - Prob. 33RECh. 15 - With the aid of Exercise 33, determine whether F...Ch. 15 - As discussed in Example 1 of Section 15.1,...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Simplify.

Pre-Algebra Student Edition

17. Randomness When using a computer to randomly generate the last digit of a phone number to be called for a s...

Elementary Statistics (13th Edition)

In Exercises 1–10, find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. 1.

University Calculus: Early Transcendentals (4th Edition)

Applying the Empirical Rule with z-Scores The Empirical Rule applies rough approximations to probabilities for ...

Introductory Statistics

ASSESSMENT A sheet of paper is cut into 5 same-size parts. Each of the parts is then cut into 5 same-size parts...

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

Twenty five people, consisting of 15 women and 10 men are lined up in a random order. Find the probability that...

A First Course in Probability (10th Edition)

Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Text book image
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
SEE MORE TEXTBOOKS
Quadrilaterals: Missing Angles and Sides; Author: rhornfeck;https://www.youtube.com/watch?v=knVj1O0L2TM;License: Standard YouTube License, CC-BY
STD IX | State Board | Types of Quadrilateral; Author: Robomate;https://www.youtube.com/watch?v=wh0KQ4UB0EU;License: Standard YouTube License, CC-BY