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(2) Evaluate the line integral of f(x, y) = y + x along the following paths in the xy-plane. (a) Straight line from (0, 1) to (1, 2). (b) Counterclockwise around the circle of radius 4 centered at the origin, starting from (4,0) and ending at (0, -4).

(2) Evaluate the line integral of f(x, y) = y + x along the following paths in the xy-plane. (a) Straight line from (0, 1) to (1, 2). (b) Counterclockwise around the circle of radius 4 centered at the origin, starting from (4,0) and ending at (0, -4).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is Vector Calculus. Please answer thoroughly with clear answers and explanations. This is a 4 part question split into two different posts. PLEASE ONLY ANSWER PARTS A AND B. Thank you

(c) Part of the parabola \( y = 2(x+1)^2 \) from the point \( (0, 2) \) to the point \( (-1, 0) \). (d) Counterclockwise around the perimeter of a triangle of area 3. Hint: If the curve \( C \) is a finite union of the smooth curves \( C_1, \cdots , C_n \) joining end to end then \[ \int_C f \, ds = \sum_{i=1}^n \int_{C_i} f \, ds. \]
Transcribed Image Text:(c) Part of the parabola \( y = 2(x+1)^2 \) from the point \( (0, 2) \) to the point \( (-1, 0) \). (d) Counterclockwise around the perimeter of a triangle of area 3. Hint: If the curve \( C \) is a finite union of the smooth curves \( C_1, \cdots , C_n \) joining end to end then \[ \int_C f \, ds = \sum_{i=1}^n \int_{C_i} f \, ds. \]
**Exercise 2: Evaluating Line Integrals** Evaluate the line integral of the function \( f(x, y) = -y + x \) along the following paths in the \( xy \)-plane: (a) **Straight Line Path:** From the point \( (0, 1) \) to the point \( (1, 2) \). (b) **Circular Path:** Move counterclockwise around a circle with a radius of 4, centered at the origin. Start the path from the point \( (4, 0) \) and end at the point \( (0, -4) \).
Transcribed Image Text:**Exercise 2: Evaluating Line Integrals** Evaluate the line integral of the function \( f(x, y) = -y + x \) along the following paths in the \( xy \)-plane: (a) **Straight Line Path:** From the point \( (0, 1) \) to the point \( (1, 2) \). (b) **Circular Path:** Move counterclockwise around a circle with a radius of 4, centered at the origin. Start the path from the point \( (4, 0) \) and end at the point \( (0, -4) \).
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