 15.2.1: The area of the surface extending upward from the linesegment y = x...
 15.2.2: Suppose that a wire has equation y = 1 x (0 x 1)and that its mass d...
 15.2.3: If C is the curve represented by the equationsx = sin t, y = cost, ...
 15.2.4: If C is the unit circle x2 + y2 = 1 oriented counterclockwiseand F(...
 15.2.5: Use (30) to explain why the line integral in part (a) ofExample 8 c...
 15.2.6: (a) Use (30) to explain why the line integral in part (b)of Example...
 15.2.7: 710 Evaluate C F dr along the line segment C from P to Q. F(x, y) =...
 15.2.8: 710 Evaluate C F dr along the line segment C from P to Q. F(x, y) =...
 15.2.9: 710 Evaluate C F dr along the line segment C from P to Q. F(x, y) =...
 15.2.10: 710 Evaluate C F dr along the line segment C from P to Q. F(x, y) =...
 15.2.11: Let C be the curve represented by the equationsx = 2t, y = t2 (0 t ...
 15.2.12: Let C be the curve represented by the equationsx = t, y = 3t2, z = ...
 15.2.13: In each part, evaluate the integralC(3x + 2y) dx + (2x y) dyalong t...
 15.2.14: In each part, evaluate the integralCy dx + z dy x dzalong the state...
 15.2.15: 1518 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.2.16: 1518 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.2.17: 1518 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.2.18: 1518 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.2.19: 1922 Evaluate the line integral with respect to s along the curve C...
 15.2.20: 1922 Evaluate the line integral with respect to s along the curve C...
 15.2.21: 1922 Evaluate the line integral with respect to s along the curve C...
 15.2.22: 1922 Evaluate the line integral with respect to s along the curve C...
 15.2.23: 2330 Evaluate the line integral along the curve C. C(x + 2y) dx + (...
 15.2.24: 2330 Evaluate the line integral along the curve C. C(x2 y2)dx + x d...
 15.2.25: 2330 Evaluate the line integral along the curve C. Cy dx + x dyC : ...
 15.2.26: 2330 Evaluate the line integral along the curve C. C(y x) dx + x2y ...
 15.2.27: 2330 Evaluate the line integral along the curve C. C(x2 + y2)dx x d...
 15.2.28: 2330 Evaluate the line integral along the curve C. C(y x) dx + xy d...
 15.2.29: 2330 Evaluate the line integral along the curve C. Cyz dx xz dy + x...
 15.2.30: 2330 Evaluate the line integral along the curve C. Cx2 dx + xy dy +...
 15.2.31: 3132 Use a CAS to evaluate the line integrals along the given curve...
 15.2.32: 3132 Use a CAS to evaluate the line integrals along the given curve...
 15.2.33: 3334 Evaluate C y dx x dy along the curve C shown in the figure. 33
 15.2.34: 3334 Evaluate C y dx x dy along the curve C shown in the figure. 34
 15.2.35: 3536 Evaluate C x2z dx yx2 dy + 3 dz along the curve C shown in the...
 15.2.36: 3536 Evaluate C x2z dx yx2 dy + 3 dz along the curve C shown in the...
 15.2.37: 3740 Evaluate C F dr along the curve C. F(x, y) = x2i + xy jC : r(t...
 15.2.38: 3740 Evaluate C F dr along the curve C. F(x, y) = x2yi + 4jC : r(t)...
 15.2.39: 3740 Evaluate C F dr along the curve C. F(x, y) = (x2 + y2)3/2(xi +...
 15.2.40: 3740 Evaluate C F dr along the curve C. F(x, y, z) = zi + x j + ykC...
 15.2.41: Find the mass of a thin wire shaped in the form of the circulararc ...
 15.2.42: Find the mass of a thin wire shaped in the form of the curvex = et ...
 15.2.43: Find the mass of a thin wire shaped in the form of the helixx = 3 c...
 15.2.44: Find the mass of a thin wire shaped in the form of the curvex = 2t,...
 15.2.45: 4548 Find the work done by the force field F on a particle thatmove...
 15.2.46: 4548 Find the work done by the force field F on a particle thatmove...
 15.2.47: 4548 Find the work done by the force field F on a particle thatmove...
 15.2.48: 4548 Find the work done by the force field F on a particle thatmove...
 15.2.49: 4950 Find the work done by the force fieldF(x, y) = 1x2 + y2 i +4x2...
 15.2.50: 4950 Find the work done by the force fieldF(x, y) = 1x2 + y2 i +4x2...
 15.2.51: 5152 Use a line integral to find the area of the surface. The surfa...
 15.2.52: 5152 Use a line integral to find the area of the surface. The surfa...
 15.2.53: As illustrated in the accompanying figure, a sinusoidal cutis made ...
 15.2.54: Evaluate the integral Cx dy y dxx2 + y2 , whereC is the circlex2 + ...
 15.2.55: Suppose that a particle moves through the force fieldF(x, y) = xyi ...
 15.2.56: A farmer weighing 150 lb carries a sack of grain weighing20 lb up a...
 15.2.57: Suppose that a curve C in the xyplane is smoothly parametrizedbyr(...
 15.2.58: Writing Discuss the similarities and differences betweenthe definit...
 15.2.59: Writing Describe the different types of line integrals, anddiscuss ...
Solutions for Chapter 15.2: LINE INTEGRALS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 15.2: LINE INTEGRALS
Get Full SolutionsSince 59 problems in chapter 15.2: LINE INTEGRALS have been answered, more than 38285 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 15.2: LINE INTEGRALS includes 59 full stepbystep solutions.

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Compound interest
Interest that becomes part of the investment

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

End behavior
The behavior of a graph of a function as.

Factored form
The left side of u(v + w) = uv + uw.

Line graph
A graph of data in which consecutive data points are connected by line segments

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Matrix element
Any of the real numbers in a matrix

Natural exponential function
The function ƒ1x2 = ex.

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

nth root
See Principal nth root

Orthogonal vectors
Two vectors u and v with u x v = 0.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Root of a number
See Principal nth root.

Vertex of a cone
See Right circular cone.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.