Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use a CAS and Green's Theorem to find the counterclockwise circulation of the field $\mathbf{F}$ around the simple closed curve $C$. Perform the following CAS steps. a. Plot $C$ in the $x y$ -plane.b. Determine the integrand $(\partial N / \partial x)-(\partial M / \partial y)$ for the tangential form of Green's Theorem.c. Determine the (double integral) limits of integration from your plot in part (a) and evaluate the curl integral for the circulation.$$\mathbf{F}=(2 x-y) \mathbf{i}+(x+3 y) \mathbf{j}, \quad C: \text { The ellipse } x^{2}+4 y^{2}=4$$

Calculus 3

Chapter 16

Integrals and Vector Fields

Section 4

Green’s Theorem in the Plane

Vector Functions

Johns Hopkins University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

08:32

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

02:07

Use a CAS and Green's…

01:01

01:31

problem or deny I don't have a CS, but I can draw a graph here. A party? If your lips and this is still zero, this is zero. What? So here's our mercy. Now we can't calculate populated part tracks, which is one minus partner Amber Hawaii. So minus minus one. Right, So just to all right, uh, I calculate you can know that this is just two times era that Iraq will be two times one times pi. So it took a lot out. There should be four pi and just to say yes, but I don't have one.

View More Answers From This Book

Find Another Textbook

03:31

The sum of three consecutive integers is $96,$ find the three integers.

01:45

Determine the center and radius of the given circle and sketch its graph.

01:15

Rewrite the equation in the form $a x^{2}+b x+c=0,$ with $a > 0,$ and the…

02:19

(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -i…

02:12

In each of the following, solve the given quadratic equation exactly using t…

02:43

02:00

Find the unknown.$$(2 r-3)^{2}-24=0$$

01:42

Compute the difference quotient $\frac{f(x+h)-f(x)}{h}, \quad h \neq 0$ When…

01:03

02:25

Solve each of the quadratics by first completing the square. When the roots …