 16.2.1: Evaluate the line integral, where is the given curve.
 16.2.2: Evaluate the line integral, where is the given curve.
 16.2.3: Evaluate the line integral, where is the given curve.
 16.2.4: Evaluate the line integral, where is the given curve.
 16.2.5: Evaluate the line integral, where is the given curve.
 16.2.6: Evaluate the line integral, where is the given curve.
 16.2.7: Evaluate the line integral, where is the given curve.
 16.2.8: Evaluate the line integral, where is the given curve.
 16.2.9: Evaluate the line integral, where is the given curve.
 16.2.10: Evaluate the line integral, where is the given curve.
 16.2.11: Evaluate the line integral, where is the given curve.
 16.2.12: Evaluate the line integral, where is the given curve.
 16.2.13: Evaluate the line integral, where is the given curve.
 16.2.14: Evaluate the line integral, where is the given curve.
 16.2.15: Evaluate the line integral, where is the given curve.
 16.2.16: Evaluate the line integral, where is the given curve.
 16.2.17: Let be the vector field shown in the figure. (a) If is the vertical...
 16.2.18: The figure shows a vector field and two curves and . Are the line i...
 16.2.19: Evaluate the line integral , where is given by the vector function .
 16.2.20: Evaluate the line integral , where is given by the vector function .
 16.2.21: Evaluate the line integral , where is given by the vector function .
 16.2.22: Evaluate the line integral , where is given by the vector function .
 16.2.23: Use a calculator or CAS to evaluate the line integral correct to fo...
 16.2.24: Use a calculator or CAS to evaluate the line integral correct to fo...
 16.2.25: Use a calculator or CAS to evaluate the line integral correct to fo...
 16.2.26: Use a calculator or CAS to evaluate the line integral correct to fo...
 16.2.27: Use a graph of the vector field F and the curve C to guess whether ...
 16.2.28: Use a graph of the vector field F and the curve C to guess whether ...
 16.2.29: (a) Evaluate the line integral , where and is given by , . ; (b) Il...
 16.2.30: (a) Evaluate the line integral , where and is given by , . ; (b) Il...
 16.2.31: Find the exact value of , where is the curve with parametric equati...
 16.2.32: (a) Find the work done by the force field on a particle that moves ...
 16.2.33: A thin wire is bent into the shape of a semicircle , . If the linea...
 16.2.34: A thin wire has the shape of the firstquadrant part of the circle ...
 16.2.35: (a) Write the formulas similar to Equations 4 for the center of mas...
 16.2.36: Find the mass and center of mass of a wire in the shape of the heli...
 16.2.37: If a wire with linear density lies along a plane curve its moments ...
 16.2.38: If a wire with linear density lies along a space curve , its moment...
 16.2.39: Find the work done by the force field in moving an object along an ...
 16.2.40: Find the work done by the force field on a particle that moves alon...
 16.2.41: Find the work done by the force field on a particle that moves alon...
 16.2.42: The force exerted by an electric charge at the origin on a charged ...
 16.2.43: The position of an object with mass at time is , . (a) What is the ...
 16.2.44: An object with mass moves with position function , . Find the work ...
 16.2.45: A 160lb man carries a 25lb can of paint up a helical staircase th...
 16.2.46: Suppose there is a hole in the can of paint in Exercise 45 and 9 lb...
 16.2.47: (a) Show that a constant force field does zero work on a particle t...
 16.2.48: The base of a circular fence with radius 10 m is given by . The hei...
 16.2.49: If is a smooth curve given by a vector function , , and is a consta...
 16.2.50: If is a smooth curve given by a vector function , , show that
 16.2.51: An object moves along the curve shown in the figure from (1, 2) to ...
 16.2.52: Experiments show that a steady current in a long wire pro  duces a...
Solutions for Chapter 16.2: LINE INTEGRALS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 16.2: LINE INTEGRALS
Get Full SolutionsThis textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 52 problems in chapter 16.2: LINE INTEGRALS have been answered, more than 21977 students have viewed full stepbystep solutions from this chapter. Chapter 16.2: LINE INTEGRALS includes 52 full stepbystep solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Circle
A set of points in a plane equally distant from a fixed point called the center

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Directed distance
See Polar coordinates.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Negative numbers
Real numbers shown to the left of the origin on a number line.

Nonsingular matrix
A square matrix with nonzero determinant

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Polar form of a complex number
See Trigonometric form of a complex number.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Row operations
See Elementary row operations.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Xmin
The xvalue of the left side of the viewing window,.