a) To show that 1 2 ∫ C − y d x + x d y = 1 2 ( x 1 y 2 − x 2 y 1 ) if C be the line segment joining ( x 1 , y 1 ) and ( x 2 , y 2 ) .

Question

Want to see the full answer?

Answer 1

Question

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

2\int_{-3/2}^{3/2} \sqrt{4u^2+2} du

2. Consider the following: Prove that x, x2, and 1/x are the solutions to the homogeneous equation corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4. b. use variation of parameters to find a particular solution and complete the general solution to the differential equation. I am interested in process. You may use a computer for integration, finding determinants and doing Kramer's.

3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.

Answer 2

Question

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Answer 6

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

Answer 7

Chapter 18.1, Problem 36E

To determine

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

Answer 8

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Answer 9

To determine

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 13

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

a) To show that 1 2 ∫ C − y d x + x d y = 1 2 ( x 1 y 2 − x 2 y 1 ) if C be the line segment joining ( x 1 , y 1 ) and ( x 2 , y 2 ) .

Solution Summary: The author explains that the parametrization of the line joining ( x 1, y 1) and (x 2.

Videos

a)

To show that $\frac{1}{2} \int_{C} - y d x + x d y = \frac{1}{2} (x_{1} y_{2} - x_{2} y_{1})$ if $C$ be the line segment joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

b)

To prove that the area of the polygon with vertices $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ ,……. $(x_{n}, y_{n})$ is equal to $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

Want to see the full answer?

Chapter 18 Solutions

a) To show that 1 2 ∫ C − y d x + x d y = 1 2 ( x 1 y 2 − x 2 y 1 ) if C be the line segment joining ( x 1 , y 1 ) and ( x 2 , y 2 ) .

Solution Summary: The author explains that the parametrization of the line joining ( x 1, y 1) and (x 2.

Videos