Sketch the region D bounded by the curves y = 2 x , y = 1 2 x , y = 2 x , y = x 2 in the first quadrant. (a) The image of D under F (b) Show that | J a c ( G ) | = 1 2 | v | (c) Prove the formula by applying the change of variables formula ∫ ∫ D f ( y x ) d x d y = 3 4 ∫ 1 / 2 2 f ( v ) d v v (d) Evaluate ∫ ∫ D y e y x x d x d y

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Answer 1

Question

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

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Answer 2

Question

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Expert Solution & Answer

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Answer 3

Question

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Expert Solution & Answer

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Answer 5

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Answer 6

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Answer 7

Chapter 16, Problem 61CRE

To determine

To calculate:

Sketch the region $D$ bounded by the curves $y = \frac{2}{x}, y = \frac{1}{2 x}, y = 2 x, y = \frac{x}{2}$ in the first quadrant.

(a) The image of $D$ under $F$

(b) Show that $| J a c (G) | = \frac{1}{2 | v |}$

(c) Prove the formula by applying the change of variables formula

$\int \int_{D} f (\frac{y}{x}) d x d y = \frac{3}{4} \int_{1 / 2}^{2} \frac{f (v) d v}{v}$

(d) Evaluate $\int \int_{D} \frac{y e^{\frac{y}{x}}}{x} d x d y$

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

Solution Summary: The author illustrates how the region is sketched as shown in the Figure.

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Chapter 16 Solutions

Solution Summary: The author illustrates how the region is sketched as shown in the Figure.

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To calculate: Sketch the region Dbounded by the curves y=2x,y=12x,y=2x,y=x2 in the first quadrant. (a) The image of Dunder F (b) Show that |Jac(G)|=12|v| (c) Prove the formula by applying the change of variables formula ∫∫Df(yx)dxdy=34∫1/22f(v)dvv (d) Evaluate ∫∫Dyeyxxdxdy

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Chapter 16 Solutions