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

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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 $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

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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 $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

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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 $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

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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 $\frac{1}{2} \sum_{i = 1}^{n} x_{i} y_{i + 1} - x_{i + 1} y_{i}$

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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

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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