Question 1

Evaluate the line integral over the given curve C.

Accepted Answer

The answer of Evaluate the line integral over the given...

Question 2

Show that F is conservative, and find a function f such that   and use the result to evaluate   where C is any curve from     Select the correct Answer

Accepted Answer

A) -89 
B) 0 
C) -154 
D) -107 
A) -89 
B) 0 
C) -154 
D) -107

Question 3

Show that F is conservative and find a function   such that   and use this result to evaluate   where C is any path from

Accepted Answer

The answer of Show that F is conservative and find...

Question 4

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find   where a is the constant vector.

Accepted Answer

The answer of Assuming that S satisfies the conditions of...

Question 5

A thin wire is bent into the shape of a semicircle   If the linear density is , find the exact mass of the wire.Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Evaluate the surface integral where S is the surface with parametric equations     Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Select the correct Answer for each question.
-Evaluate the line integral   where   and C is the arc of the circle   traversed counterclockwise from   , 0) to   Round yourAnswer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Use Green's Theorem to find the work done by the force   in moving a particle in the positive direction once around the triangle with vertices   and   Select the correct Answer

Accepted Answer

A) 7 
B)    
C)    
D) 42 
A) 7 
B)    
C)    
D) 42

Question 9

Find parametric equations for C, if C is the curve of intersection of the hyperbolic paraboloid   and the cylinder   oriented counterclockwise as viewed from above.

Accepted Answer

The answer of Find parametric equations for C, if C...

Question 10

Find the exact mass of a thin wire in the shape of the helix   if the density is 5.Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Select the correct Answer for each question.
-Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Evaluate the surface integral where S is the surface with parametric equations

Accepted Answer

The answer of Evaluate the surface integral where S is...

Question 13

Let S be the cube with vertices   Approximate   by using a Riemann sum as in Definition 1, taking the patches   to be the squares that are the faces of the cube and the points   to be the centers of the squares.

Accepted Answer

The answer of Let S be the cube with vertices...

Question 14

Select the correct Answer for each question.
-Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find   where a is the constant vector.

Accepted Answer

A) 8 
B) 6 
C) 5 
D) 7 
E) 0 
A) 8 
B) 6 
C) 5 
D) 7 
E) 0

Question 15

Select the correct Answer for each question.
-Let

Accepted Answer

A) 5 
B) 3 
C) 1 
D) 2 
E) None of these 
A) 5 
B) 3 
C) 1 
D) 2 
E) None of these

Question 16

Find the gradient vector field of the scalar function   (That is, find the conservative vector field F for the potential function   of F.)

Accepted Answer

The answer of Find the gradient vector field of the...

Question 17

Evaluate the surface integral.Round yourAnswer to four decimal places.   S is surface   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find the area of the surface S where S is the part of the sphere   that lies to the right of the xz-plane and inside the cylinder

Accepted Answer

The answer of Find the area of the surface S...

Question 19

Select the correct Answer for each question.
-Show that F is conservative, and find a function f such that   and use the result to evaluate   where C is any curve from

Accepted Answer

A) 0 
B) -154 
C) -107 
D) -89 
A) 0 
B) -154 
C) -107 
D) -89

Question 20

Find the mass of the surface S having the given mass density.S is part of the plane   in the first octant; the density at a point P on S is equal to the square of the distance between P and the xy-plane.

Accepted Answer

The answer of Find the mass of the surface S...

Evaluate the line integral over the given curve C.

Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from Select the correct Answer

Show that F is conservative and find a function such that and use this result to evaluate where C is any path from

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

A thin wire is bent into the shape of a semicircle If the linear density is , find the exact mass of the wire.Select the correct Answer

Evaluate the surface integral where S is the surface with parametric equations Select the correct Answer

Select the correct Answer for each question. -Evaluate the line integral where and C is the arc of the circle traversed counterclockwise from , 0) to Round yourAnswer to two decimal places.

Use Green's Theorem to find the work done by the force in moving a particle in the positive direction once around the triangle with vertices and Select the correct Answer

Find parametric equations for C, if C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find the exact mass of a thin wire in the shape of the helix if the density is 5.Select the correct Answer

Select the correct Answer for each question. -Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Evaluate the surface integral where S is the surface with parametric equations

Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

Select the correct Answer for each question. -Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

Select the correct Answer for each question. -Let

Find the gradient vector field of the scalar function (That is, find the conservative vector field F for the potential function of F.)

Evaluate the surface integral.Round yourAnswer to four decimal places. S is surface Select the correct Answer

Find the area of the surface S where S is the part of the sphere that lies to the right of the xz-plane and inside the cylinder

Select the correct Answer for each question. -Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from

Find the mass of the surface S having the given mass density.S is part of the plane in the first octant; the density at a point P on S is equal to the square of the distance between P and the xy-plane.

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Applications of Integration

Techniques of Integration

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Exam 16: Vector Calculus

Evaluate the line integral over the given curve C.

Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from Select the correct Answer

Show that F is conservative and find a function such that and use this result to evaluate where C is any path from

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

A thin wire is bent into the shape of a semicircle If the linear density is , find the exact mass of the wire.Select the correct Answer

Evaluate the surface integral where S is the surface with parametric equations Select the correct Answer

Select the correct Answer for each question. -Evaluate the line integral where and C is the arc of the circle traversed counterclockwise from , 0) to Round yourAnswer to two decimal places.

Use Green's Theorem to find the work done by the force in moving a particle in the positive direction once around the triangle with vertices and Select the correct Answer

Find parametric equations for C, if C is the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.

Find the exact mass of a thin wire in the shape of the helix if the density is 5.Select the correct Answer

Select the correct Answer for each question. -Find the gradient vector field of the scalar function f.(That is, find the conservative vector field F for the potential function f of F.)

Evaluate the surface integral where S is the surface with parametric equations

Let S be the cube with vertices Approximate by using a Riemann sum as in Definition 1, taking the patches to be the squares that are the faces of the cube and the points to be the centers of the squares.

Select the correct Answer for each question. -Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find where a is the constant vector.

Select the correct Answer for each question. -Let

Find the gradient vector field of the scalar function (That is, find the conservative vector field F for the potential function of F.)

Evaluate the surface integral.Round yourAnswer to four decimal places. S is surface Select the correct Answer

Find the area of the surface S where S is the part of the sphere that lies to the right of the xz-plane and inside the cylinder

Select the correct Answer for each question. -Show that F is conservative, and find a function f such that and use the result to evaluate where C is any curve from

Find the mass of the surface S having the given mass density.S is part of the plane in the first octant; the density at a point P on S is equal to the square of the distance between P and the xy-plane.

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Second-Order Differential Equations

Filters