Chapter 14: Q 6 (page 1153)

Divergence Theorem: Suppose $W$ is a region in $R^{3}$ bounded by a or surface $S$ . If localid="1651073056695" $F (x, y z)$ is defined on an open region containing $W$ , then
localid="1651150868395" $\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S}d S$
where $n$ is the outwards.

Short Answer

Expert verified

The required answer is :-

Divergence Theorem: Suppose $W$ is a region in $R^{3}$ bounded by a smooth or piecewise-smooth closed oriented surface $S$ . If $F (x, y, z)$ is defined on an open region containing $W$ , then

localid="1651153720741" $\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S} F (x, y, z) \cdot n d S .$

where $n$ is the outwards unit normal vector .

Step by step solution

Step 1. Given Information

We have given the following statement of Divergence Theorem :-

Divergence Theorem: Suppose W is a region in R3 bounded by a or surface S . If F(x, yz) is defined on an open region containing W, then

$\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S}______d S$

where $n$ is the outwards______.

We have to complete this statement.

Step 2. Complete the statement

We have to complete the given statement of Divergence Theorem.

By using the Divergence Theorem, we can complete the given statement as following :-

Divergence Theorem: Suppose $W$ is a region in $R^{3}$ bounded by a smooth or piecewise-smooth closed oriented surface $S$ . If is defined on an open region containing $W$ , then

role="math" localid="1651153700977" $\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S} F (x, y, z) \cdot n d S$

where $n$ is the outwards unit normal vector.

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Divergence Theorem: Suppose $W$ is a region in $R^{3}$ bounded by a or surface $S$ . If localid="1651073056695" $F (x, y z)$ is defined on an open region containing $W$ , then
localid="1651150868395" $\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S}d S$
where $n$ is the outwards.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

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Divergence Theorem: Suppose Wis a region in R3bounded by a ______ or ______ surface S. If localid="1651073056695" Fx,yzis defined on an open region containingW, thenlocalid="1651150868395" ∬∫WdivFx,y,zdV=∫∫S______dSwhere nis the outwards______.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Statistics

Calculus

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Divergence Theorem: Suppose $W$ is a region in $R^{3}$ bounded by a or surface $S$ . If localid="1651073056695" $F (x, y z)$ is defined on an open region containing $W$ , then
localid="1651150868395" $\iint \int_{W} d i v F (x, y, z) d V = \int \int_{S}d S$
where $n$ is the outwards.