 6.2.1: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.2: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.3: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.4: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.5: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.6: In Exercises 16, verify Greens theorem for the given vector field F...
 6.2.7: (a) Use Greens theorem to calculate the line integral C y2 dx + x 2...
 6.2.8: Let F = 3x y i + 2x 2 j and suppose C is the oriented curve shown i...
 6.2.9: Evaluate C (x 2 y2 ) dx + (x 2 + y2 ) dy, where C is the boundary o...
 6.2.10: Use Greens theorem to find the work done by the vector field F = (4...
 6.2.11: Verify that the area of the rectangle R = [0, a] [0, b] is ab, by c...
 6.2.12: Let a be a positive constant. Use Greens theorem to calculate the a...
 6.2.13: Evaluate C(x 4 y5 2y) dx + (3x + x 5 y4) dy, where C is the oriente...
 6.2.14: Use Greens theorem to find the area enclosed by the hypocycloid x(t...
 6.2.15: (a) Sketch the curve given parametrically by x(t) = (1 t 2, t 3 t)....
 6.2.16: Use Greens theorem to find the area between the ellipse x 2/9 + y2/...
 6.2.17: Show that if D is a region to which Greens theorem applies, and D i...
 6.2.18: Find the area inside the quadrilateral whose vertices taken counter...
 6.2.19: Suppose that the successive vertices of an nsided polygon are the ...
 6.2.20: Let a be a positive integer throughout this problem. An epicycloid ...
 6.2.21: Evaluate the line integral C 5y dx 3x dy, where C is the cardioid w...
 6.2.22: (a) Suppose that C is a simple, closed curve that does not enclose ...
 6.2.23: (a) Use the divergence theorem (Theorem 2.3) to show that C F n ds ...
 6.2.24: Let F = M(x, y) i + N(x, y) j. The divergence theorem shows that th...
 6.2.25: Let C be any simple, closed curve in the plane. Show that C 3x 2 y ...
 6.2.26: Show that C y3 dx + (x 3 + 2x + y) dy is positive for any closed cu...
 6.2.27: Show that if C is the boundary of any rectangular region in R2, the...
 6.2.28: Let r = x i + y j be the position vector of any point in the plane....
 6.2.29: Let D be a region to which Greens theorem applies and suppose that ...
 6.2.30: Let f (x, y) be a function of class C2 such that 2 f x 2 + 2 f y2 =...
 6.2.31: Let D be a region to which Greens theorem applies and n the outward...
Solutions for Chapter 6.2: Greens Theorem
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 6.2: Greens Theorem
Get Full SolutionsVector Calculus was written by and is associated to the ISBN: 9780321780652. Since 31 problems in chapter 6.2: Greens Theorem have been answered, more than 13616 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Chapter 6.2: Greens Theorem includes 31 full stepbystep solutions.

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

Augmented matrix
A matrix that represents a system of equations.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Graphical model
A visible representation of a numerical or algebraic model.

Inverse cotangent function
The function y = cot1 x

Local extremum
A local maximum or a local minimum

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Normal curve
The graph of ƒ(x) = ex2/2

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Pie chart
See Circle graph.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Real part of a complex number
See Complex number.

Venn diagram
A visualization of the relationships among events within a sample space.

Ymax
The yvalue of the top of the viewing window.