 15.2.1: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.2: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.3: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.4: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.5: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.6: In Exercises 16, find a piecewise smooth parametrization of the pat...
 15.2.7: In Exercises 710, evaluate the line integral along the given path.
 15.2.8: In Exercises 710, evaluate the line integral along the given path.
 15.2.9: In Exercises 710, evaluate the line integral along the given path.
 15.2.10: In Exercises 710, evaluate the line integral along the given path.
 15.2.11: In Exercises 1114, evaluate along the given path.
 15.2.12: In Exercises 1114, evaluate along the given path.
 15.2.13: In Exercises 1114, evaluate along the given path.
 15.2.14: In Exercises 1114, evaluate along the given path.
 15.2.15: In Exercises 1518, evaluate along the given path.
 15.2.16: In Exercises 1518, evaluate along the given path.
 15.2.17: In Exercises 1518, evaluate along the given path.
 15.2.18: In Exercises 1518, evaluate along the given path.
 15.2.19: In Exercises 19 and 20, evaluate along the path shown in the figure.
 15.2.20: In Exercises 19 and 20, evaluate along the path shown in the figure.
 15.2.21: Mass In Exercises 21 and 22, find the total mass of two turns of a ...
 15.2.22: Mass In Exercises 21 and 22, find the total mass of two turns of a ...
 15.2.23: Mass In Exercises 2326, find the total mass of the wire with density
 15.2.24: Mass In Exercises 2326, find the total mass of the wire with density
 15.2.25: Mass In Exercises 2326, find the total mass of the wire with density
 15.2.26: Mass In Exercises 2326, find the total mass of the wire with density
 15.2.27: In Exercises 2732, evaluate where is represented by
 15.2.28: In Exercises 2732, evaluate where is represented by
 15.2.29: In Exercises 2732, evaluate where is represented by
 15.2.30: In Exercises 2732, evaluate where is represented by
 15.2.31: In Exercises 2732, evaluate where is represented by
 15.2.32: In Exercises 2732, evaluate where is represented by
 15.2.33: In Exercises 33 and 34, use a computer algebra system to evaluate t...
 15.2.34: In Exercises 33 and 34, use a computer algebra system to evaluate t...
 15.2.35: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.36: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.37: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.38: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.39: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.40: Work In Exercises 3540, find the work done by the force field F on ...
 15.2.41: Work Find the work done by a person weighing 150 pounds walking exa...
 15.2.42: Work A particle moves along the path from the point to the point Th...
 15.2.43: In Exercises 43 and 44, evaluate for each curve. Discuss the orient...
 15.2.44: In Exercises 43 and 44, evaluate for each curve. Discuss the orient...
 15.2.45: In Exercises 45 48, demonstrate the property that regardless of the...
 15.2.46: In Exercises 45 48, demonstrate the property that regardless of the...
 15.2.47: In Exercises 45 48, demonstrate the property that regardless of the...
 15.2.48: In Exercises 45 48, demonstrate the property that regardless of the...
 15.2.49: In Exercises 4952, evaluate the line integral along the path given ...
 15.2.50: In Exercises 4952, evaluate the line integral along the path given ...
 15.2.51: In Exercises 4952, evaluate the line integral along the path given ...
 15.2.52: In Exercises 4952, evaluate the line integral along the path given ...
 15.2.53: In Exercises 5360, evaluate the integral along the path C.
 15.2.54: In Exercises 5360, evaluate the integral along the path C.
 15.2.55: In Exercises 5360, evaluate the integral along the path C.
 15.2.56: In Exercises 5360, evaluate the integral along the path C.
 15.2.57: In Exercises 5360, evaluate the integral along the path C.
 15.2.58: In Exercises 5360, evaluate the integral along the path C.
 15.2.59: In Exercises 5360, evaluate the integral along the path C.
 15.2.60: In Exercises 5360, evaluate the integral along the path C.
 15.2.61: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.62: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.63: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.64: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.65: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.66: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.67: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.68: Lateral Surface Area In Exercises 6168, find the area of the latera...
 15.2.69: Engine Design A tractor engine has a steel component with a circula...
 15.2.70: Building Design The ceiling of a building has a height above the fl...
 15.2.71: Moments of Inertia Consider a wire of density given by the space cu...
 15.2.72: Moments of Inertia Consider a wire of density given by the space cu...
 15.2.73: Approximation In Exercises 73 and 74, determine which value best ap...
 15.2.74: Approximation In Exercises 73 and 74, determine which value best ap...
 15.2.75: Investigation The top outer edge of a solid with vertical sides and...
 15.2.76: Investigation Determine the value of such that the work done by the...
 15.2.77: Define a line integral of a function along a smooth curve in the pl...
 15.2.78: Define a line integral of a continuous vector field on a smooth cur...
 15.2.79: Order the surfaces in ascending order of the lateral surface area u...
 15.2.80: For each of the following, determine whether the work done in movin...
 15.2.81: True or False? In Exercises 8184, determine whether the statement i...
 15.2.82: True or False? In Exercises 8184, determine whether the statement i...
 15.2.83: True or False? In Exercises 8184, determine whether the statement i...
 15.2.84: True or False? In Exercises 8184, determine whether the statement i...
 15.2.85: Work Consider a particle that moves through the force field from th...
Solutions for Chapter 15.2: Line Integrals
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 15.2: Line Integrals
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780618502981. Chapter 15.2: Line Integrals includes 85 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 85 problems in chapter 15.2: Line Integrals have been answered, more than 77842 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Acute angle
An angle whose measure is between 0° and 90°

Addition property of equality
If u = v and w = z , then u + w = v + z

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Differentiable at x = a
ƒ'(a) exists

Elimination method
A method of solving a system of linear equations

Inductive step
See Mathematical induction.

Initial side of an angle
See Angle.

Initial value of a function
ƒ 0.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Limit to growth
See Logistic growth function.

Line of travel
The path along which an object travels

Linear system
A system of linear equations

Nonsingular matrix
A square matrix with nonzero determinant

nth root of unity
A complex number v such that vn = 1

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

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

Unit ratio
See Conversion factor.

Whole numbers
The numbers 0, 1, 2, 3, ... .