 9.8.1: In 14, evaluate fc G(x, y) dx, fc G(x, y) dy, and fc G(x, y) ds on...
 9.8.2: In 14, evaluate fc G(x, y) dx, fc G(x, y) dy, and fc G(x, y) ds on...
 9.8.3: In 14, evaluate fc G(x, y) dx, fc G(x, y) dy, and fc G(x, y) ds on...
 9.8.4: In 14, evaluate fc G(x, y) dx, fc G(x, y) dy, and fc G(x, y) ds on...
 9.8.5: In 5 and 6, evaluate fc G(x, y, z) dx, f c G(x, y, z) dy, fc G(x, y...
 9.8.6: In 5 and 6, evaluate fc G(x, y, z) dx, f c G(x, y, z) dy, fc G(x, y...
 9.8.7: In 710, evaluate fc (2x + y) dx + xy dy on the given curve C betwe...
 9.8.8: In 710, evaluate fc (2x + y) dx + xy dy on the given curve C betwe...
 9.8.9: In 710, evaluate fc (2x + y) dx + xy dy on the given curve C betwe...
 9.8.10: In 710, evaluate fc (2x + y) dx + xy dy on the given curve C betwe...
 9.8.11: In 1114, evaluate fcY dx + x dy on the given curve C between (0, 0...
 9.8.12: In 1114, evaluate fcY dx + x dy on the given curve C between (0, 0...
 9.8.13: In 1114, evaluate fcY dx + x dy on the given curve C between (0, 0...
 9.8.14: In 1114, evaluate fcY dx + x dy on the given curve C between (0, 0...
 9.8.15: Evaluate f c (6x2 + 2y2) dx + 4.xy dy, where C is given by x = Vt, ...
 9.8.16: Evaluate f c y2 dx + xy dy, where C is given by x = 2t, y = t3' 0 ...
 9.8.17: Evaluate f c 2x3y dx + (3x + y) dy, where C is given by x = y2 from...
 9.8.18: Evaluate f c 4x dx + 2y dy, where C is given by x = y3 + 1 from (0,...
 9.8.19: In 19 and 20, evaluate Pc (x2 + y2) dx  2xy dy on the given closed...
 9.8.20: In 19 and 20, evaluate Pc (x2 + y2) dx  2xy dy on the given closed...
 9.8.21: In 21and22, evaluate Pc x2y3 dx xy2 dy on the given closed curve C...
 9.8.22: In 21and22, evaluate Pc x2y3 dx xy2 dy on the given closed curve C...
 9.8.23: Evaluate Pc (x2 y2) ds, where C is given by x = 5 cos t, y = 5 sin...
 9.8.24: Evaluate fc y dx  x dy, where C is given by x = 2 cost, y = 3 sin...
 9.8.25: In 2528, evaluate f c y dx + z dy + x dz on the given curve C betw...
 9.8.26: In 2528, evaluate f c y dx + z dy + x dz on the given curve C betw...
 9.8.27: In 2528, evaluate f c y dx + z dy + x dz on the given curve C betw...
 9.8.28: In 2528, evaluate f c y dx + z dy + x dz on the given curve C betw...
 9.8.29: In 29 and 30, evaluate f c F dr. F(x, y) =y 3i x2yj; r(t) = e21i ...
 9.8.30: In 29 and 30, evaluate f c F dr. F(x, y, z) = exi + xexyj + xyexYk'...
 9.8.31: Find the work done by the force F(x, y) = yi + xj acting along y = ...
 9.8.32: Find the work done by the force F(x, y) = 2xyi + 4y2j acting along ...
 9.8.33: Find the work done by the force F(x, y) = (x + 2y)i + (6y  2x)j ac...
 9.8.34: Findtheworkdoneby theforceF(x,y,z) = yzi + xzj + xyk acting along t...
 9.8.35: Find the work done by a constant force F(x, y) = ai + bj acting cou...
 9.8.36: In an inverse square force field F = cr!llrll3, where c is a consta...
 9.8.37: Verifythatthelineintegral fcy2 dx + xydy has the same value on C fo...
 9.8.38: Consider the three curves between (0, 0) and (2, 4): c,:x=t, y=2t, ...
 9.8.39: Assume a smooth curve C is described by the vector function r(t) fo...
 9.8.40: If p(x, y) is the density of a wire (mass per unit length), then m ...
 9.8.41: The coordinates of the center of mass of a wire with variable densi...
 9.8.42: A force field F(x, y) acts at each point on the curve C, which is t...
Solutions for Chapter 9.8: Line Integrals
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 9.8: Line Integrals
Get Full SolutionsChapter 9.8: Line Integrals includes 42 full stepbystep solutions. Since 42 problems in chapter 9.8: Line Integrals have been answered, more than 33044 students have viewed full stepbystep solutions from this chapter. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Central composite design (CCD)
A secondorder response surface design in k variables consisting of a twolevel factorial, 2k axial runs, and one or more center points. The twolevel factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a secondorder model.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Density function
Another name for a probability density function

Dispersion
The amount of variability exhibited by data

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Error variance
The variance of an error term or component in a model.

Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Exponential random variable
A series of tests in which changes are made to the system under study

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .