 15.2.1: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.2: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.3: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.4: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.5: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.6: In Exercises 16, find a piecewise smooth parametrization ofthe path...
 15.2.7: In Exercises 710, evaluate the line integral along the givenpath.
 15.2.8: In Exercises 710, evaluate the line integral along the givenpath.
 15.2.9: In Exercises 710, evaluate the line integral along the givenpath.
 15.2.10: In Exercises 710, evaluate the line integral along the givenpath.
 15.2.11: In Exercises 1114, (a) find a parametrization of the path and(b) ev...
 15.2.12: In Exercises 1114, (a) find a parametrization of the path and(b) ev...
 15.2.13: In Exercises 1114, (a) find a parametrization of the path and(b) ev...
 15.2.14: In Exercises 1114, (a) find a parametrization of the path and(b) ev...
 15.2.15: In Exercises 1518, (a) find a parametrization of the pathand (b) ev...
 15.2.16: In Exercises 1518, (a) find a parametrization of the pathand (b) ev...
 15.2.17: In Exercises 1518, (a) find a parametrization of the pathand (b) ev...
 15.2.18: In Exercises 1518, (a) find a parametrization of the pathand (b) ev...
 15.2.19: In Exercises 19 and 20, (a) find a piecewise smooth parametrization...
 15.2.20: In Exercises 19 and 20, (a) find a piecewise smooth parametrization...
 15.2.21: Mass In Exercises 21 and 22, find the total mass of two turnsof a s...
 15.2.22: Mass In Exercises 21 and 22, find the total mass of two turnsof a s...
 15.2.23: Mass In Exercises 2326, find the total mass of the wire withdensity...
 15.2.24: Mass In Exercises 2326, find the total mass of the wire withdensity...
 15.2.25: Mass In Exercises 2326, find the total mass of the wire withdensity...
 15.2.26: Mass In Exercises 2326, find the total mass of the wire withdensity...
 15.2.27: In Exercises 2732, evaluate CF dr where is represented by rt t 1Fx,...
 15.2.28: In Exercises 2732, evaluate CF dr where is represented by rt Fx, y ...
 15.2.29: In Exercises 2732, evaluate CF dr where is represented by rt Fx, y ...
 15.2.30: In Exercises 2732, evaluate CF dr where is represented by rt Fx, y ...
 15.2.31: In Exercises 2732, evaluate CF dr where is represented by rt Fx, y,...
 15.2.32: In Exercises 2732, evaluate CF dr where is represented by rtFx, y, ...
 15.2.33: In Exercises 33 and 34, use a computer algebra system toevaluate th...
 15.2.34: In Exercises 33 and 34, use a computer algebra system toevaluate th...
 15.2.35: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.36: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.37: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.38: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.39: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.40: Work In Exercises 3540, find the work done by the force fieldF on a...
 15.2.41: In Exercises 41 44, determine whether the work done along thepath i...
 15.2.42: In Exercises 41 44, determine whether the work done along thepath i...
 15.2.43: In Exercises 41 44, determine whether the work done along thepath i...
 15.2.44: In Exercises 41 44, determine whether the work done along thepath i...
 15.2.45: In Exercises 45 and 46, evaluate for each curve.Discuss the orienta...
 15.2.46: In Exercises 45 and 46, evaluate for each curve.Discuss the orienta...
 15.2.47: In Exercises 47 50, demonstrate the property thatregardless of the ...
 15.2.48: In Exercises 47 50, demonstrate the property thatregardless of the ...
 15.2.49: In Exercises 47 50, demonstrate the property thatregardless of the ...
 15.2.50: In Exercises 47 50, demonstrate the property thatregardless of the ...
 15.2.51: In Exercises 5154, evaluate the line integral along the pathgiven b...
 15.2.52: In Exercises 5154, evaluate the line integral along the pathgiven b...
 15.2.53: In Exercises 5154, evaluate the line integral along the pathgiven b...
 15.2.54: In Exercises 5154, evaluate the line integral along the pathgiven b...
 15.2.55: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.56: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.57: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.58: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.59: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.60: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.61: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.62: In Exercises 5562, evaluate the integral C2x y dx 1 x 1 3y dy along...
 15.2.63: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.64: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.65: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.66: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.67: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.68: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.69: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.70: Lateral Surface Area In Exercises 6370, find the area of thelateral...
 15.2.71: Engine Design A tractor engine has a steel component witha circular...
 15.2.72: Building Design The ceiling of a building has a height abovethe flo...
 15.2.73: In Exercises 73 and 74, find the moments of inertia for the wireof ...
 15.2.74: In Exercises 73 and 74, find the moments of inertia for the wireof ...
 15.2.75: Investigation The top outer edge of a solid with vertical sidesand ...
 15.2.76: 76. Work A particle moves along the path from the pointto the point...
 15.2.77: Work Find the work done by a person weighing 175 poundswalking exac...
 15.2.78: Investigation Determine the value of such that the workdone by the ...
 15.2.79: Define a line integral of a function along a smooth curvein the pla...
 15.2.80: Define a line integral of a continuous vector field on asmooth curv...
 15.2.81: Order the surfaces in ascending order of the lateral surfacearea un...
 15.2.82: For each of the following, determine whether the work donein moving...
 15.2.83: True or False? In Exercises 8386, determine whether thestatement is...
 15.2.84: True or False? In Exercises 8386, determine whether thestatement is...
 15.2.85: True or False? In Exercises 8386, determine whether thestatement is...
 15.2.86: True or False? In Exercises 8386, determine whether thestatement is...
 15.2.87: Work Consider a particle that moves through the force fieldfrom the...
Solutions for Chapter 15.2: Line Integrals
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 15.2: Line Integrals
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. Chapter 15.2: Line Integrals includes 87 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 87 problems in chapter 15.2: Line Integrals have been answered, more than 63101 students have viewed full stepbystep solutions from this chapter.

Axis of symmetry
See Line of symmetry.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Commutative properties
a + b = b + a ab = ba

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Dependent variable
Variable representing the range value of a function (usually y)

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Directed distance
See Polar coordinates.

DMS measure
The measure of an angle in degrees, minutes, and seconds

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Logarithmic form
An equation written with logarithms instead of exponents

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Permutation
An arrangement of elements of a set, in which order is important.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Root of an equation
A solution.

Row operations
See Elementary row operations.

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,