Program Description: Purpose of the problem is to obtain the Laplace transform F ( s ) for the function f ( t ) = sin 2 t if π ≤ t ≤ 2 π ; f ( t ) = 0 if t < π or if t > 2 π .

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Answer 1

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Chapter 7.5, Problem 16P

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Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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42.37590 is correct and 42.11205 is incorect.

3. (i) Using the definition of the line integral of a vector field, calculate the line integral L³ F.dy of the vector field F: R² → R² given by F(x, y) = (y, x), and where the curve & is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]

1. Evaluate the integral ↓ f(x, y)dxdy, of function f R² →R over the domain DC R2, where: f(x, y) = 2x + y and D is the is the triangle with vertices (0, -1), (1,0) and (0,2). Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for some a

Answer 2

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Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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Answer 3

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Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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Answer 4

Question

Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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Answer 5

Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

Answer 6

Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

Answer 7

Chapter 7.5, Problem 16P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

Answer 8

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Answer 9

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Answer 11

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

Program Description: Purpose of the problem is to obtain the Laplace transform F ( s ) for the function f ( t ) = sin 2 t if π ≤ t ≤ 2 π ; f ( t ) = 0 if t < π or if t > 2 π .

Solution Summary: The author explains how the function f(t) can be written in terms of unit step function.

Concept explainers

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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Chapter 7 Solutions

Program Description: Purpose of the problem is to obtain the Laplace transform F ( s ) for the function f ( t ) = sin 2 t if π ≤ t ≤ 2 π ; f ( t ) = 0 if t &lt; π or if t &gt; 2 π .

Solution Summary: The author explains how the function f(t) can be written in terms of unit step function.

Concept explainers

Program Description: Purpose of the problem is to obtain the Laplace transform F(s) for the function f(t)=sin2t if π≤t≤2π;f(t)=0 if t<π or if t>2π .

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Chapter 7 Solutions

Program Description: Purpose of the problem is to obtain the Laplace transform F ( s ) for the function f ( t ) = sin 2 t if π ≤ t ≤ 2 π ; f ( t ) = 0 if t < π or if t > 2 π .