To choose: The appropriate option that will complete the statement “Let F ( x , y , z ) = P i + Q j + R k have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬ S F ⋅ d S = ”.

Question

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Answer 1

Question

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

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Answer 2

Question

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

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Answer 3

Question

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

Answer 6

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.

From divergence theorem, it can be written that,

∬SF⋅dS=∭EdivFdV

Thus, the value of the integral ∬SF⋅dS is ∭EdivFdV.

Therefore, the correct option is c)_.

Answer 7

Chapter 16.9, Problem 1PT

To determine

To choose: The appropriate option that will complete the statement “Let F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation. By the Divergence theorem, ∬SF⋅dS=”.

Answer 8

Expert Solution & Answer

Answer to Problem 1PT

The correct option is c)_.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Theorem used:

Divergence theorem:

Let E be a simple solid whose boundary surface S has positive orientation. Let F(x,y,z)=Pi+Qj+Rk, where P,Q and R are component functions with continuous first partial derivatives on an open region containing E. Then ∬SF⋅dS=∭EdivFdV

Calculation:

Given that, F(x,y,z)=Pi+Qj+Rk have continuous first partial derivatives and E be a simple solid with boundary surface S that has a positive orientation.