💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade Free for 30 days
Like
Report
Use the Divergence Theorem to calculate the surface integral $ \iint_S \textbf{F} \cdot d\textbf{S} $; that is, calculate the flux of $ \textbf{F} $ across $ S $.
$ \textbf{F}(x, y, z) = (xy + 2xz) \, \textbf{i} + (x^2 + y^2) \, \textbf{j} + (xy - z^2) \, \textbf{k} $, $ S $ is the surface of the solid bounded by the cylinder $ x^2 + y^2 = 4 $ and the planes $ z = y - 2 $ and $ z = 0 $
$\iint_{S} \mathbf{F} \cdot d \mathbf{S}=12 \pi$
Calculus 3
Chapter 16
Vector Calculus
Section 9
The Divergence Theorem
Campbell University
Harvey Mudd College
Baylor University
University of Nottingham
Lectures
02:56
In mathematics, a vector (…
06:36
00:09
Use the Divergence Theorem…
00:08
12:53
00:14
06:07
03:18
10:21
Evaluate the surface integ…
07:33
$5-15$ " Use the Dive…
No transcript available
View More Answers From This Book
Find Another Textbook
In mathematics, a vector (from the Latin word "vehere" meaning &qu…
In mathematics, a vector (from the Latin "mover") is a geometric o…
Use the Divergence Theorem to calculate the surface integral $ \iint_S \text…
Use the Divergence Theorem to find the outward flux of $\mathbf{F}$ across t…
Evaluate the surface integral $ \displaystyle \iint_S \textbf{F} \cdot d\tex…
$5-15$ " Use the Divergence Theorem to calculate the surfaceintegra…
01:56
Use a calculator to find the length of the curve correct to four decimal pla…
01:22
Solve the differential equation.
$ y'' - 6y' + 9y = 0…
Find the area of the part of the sphere $ x^2 + y^2 + z^2 = a^2 $ that lies …
Find the center of mass of the hemisphere $ x^2 + y^2 + z^2 = a^2 $, $ z \ge…
01:39
(a) Find the eccentricity, (b) identify the conic, (c) give an equation of t…
Let $ \textbf{F}(x, y, z) = z \tan^{-1}(y^2) \, \textbf{i} + z^3 \ln(x^2 + 1…
09:03
Solve the differential equation or initial-value problem using the method of…
04:12
In Exercises 17-34, sketch the graph of the quadratic function without using…
01:23
Find an equation for the conic that satisfies the given conditions.
…
02:46
Create an account to get free access
Join Numerade as a
By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy
or sign in with
Already have an account? Log in
