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5. Let F(x, y, z) = (2x + y, x+y, z2). Compute the following line integrals (a) JF. dr, where C is the line segment from (0, 0, 0) to (1, 1, 1). (b) F. dr, where C is the line segment from (0, 0, 1) to (1, 1, 1). (c) fF.dr, where C is the line segment from (0, 0, 0) to (1,1,0).

5. Let F(x, y, z) = (2x + y, x+y, z2). Compute the following line integrals (a) JF. dr, where C is the line segment from (0, 0, 0) to (1, 1, 1). (b) F. dr, where C is the line segment from (0, 0, 1) to (1, 1, 1). (c) fF.dr, where C is the line segment from (0, 0, 0) to (1,1,0).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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5. Let F(x, y, z) = (2x + y, x + y, z²). Compute the following line integrals: (a) SF. dr, where C is the line segment from (0,0,0) to (1, 1, 1). (b) F. dr, where C is the line segment from (0, 0, 1) to (1, 1, 1). (c) fF.dr, where C is the line segment from (0, 0, 0) to (1,1,0). (d) fF.dr, where C is the curve of intersection between the plane x + 2y + z = 3 and the cylinder x² + y² = 1, oriented counterclockwise as viewed from above. Include any necessary figures in your solution. Hint: You can use the parameterization r(t) = (x(t), y(t), z(t)) for each line segment or curve of inter- section, and then use the formula fc F. dr = f F (r(t)) - r' (t), dt.
Transcribed Image Text:5. Let F(x, y, z) = (2x + y, x + y, z²). Compute the following line integrals: (a) SF. dr, where C is the line segment from (0,0,0) to (1, 1, 1). (b) F. dr, where C is the line segment from (0, 0, 1) to (1, 1, 1). (c) fF.dr, where C is the line segment from (0, 0, 0) to (1,1,0). (d) fF.dr, where C is the curve of intersection between the plane x + 2y + z = 3 and the cylinder x² + y² = 1, oriented counterclockwise as viewed from above. Include any necessary figures in your solution. Hint: You can use the parameterization r(t) = (x(t), y(t), z(t)) for each line segment or curve of inter- section, and then use the formula fc F. dr = f F (r(t)) - r' (t), dt.
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