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1. Let f(x, y) = x² + 2y² and C be the curve along y = x³ from (0, 0) to (2,8). Find each of the following: (a) f(x,y) ds (Setup but do NOT evaluate) (b) fc f(x,y) dy (Evaluate, should get 5408/15) (c) fc f(x,y) dx (Evaluate, should get 824/21) 2. Let F = (x² + 2y², x² + 2y²) and C be the same curve as in number 1. Find L.F. Then show this is the same as 1b+1c and explain why. F.dr.

1. Let f(x, y) = x² + 2y² and C be the curve along y = x³ from (0, 0) to (2,8). Find each of the following: (a) f(x,y) ds (Setup but do NOT evaluate) (b) fc f(x,y) dy (Evaluate, should get 5408/15) (c) fc f(x,y) dx (Evaluate, should get 824/21) 2. Let F = (x² + 2y², x² + 2y²) and C be the same curve as in number 1. Find L.F. Then show this is the same as 1b+1c and explain why. F.dr.

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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Please only answer question 2. Question 1 includes the necessary information for question 2 and is why it is included.

1. Let f(x, y) = x² + 2y² and C be the curve along y = r³ from (0, 0) to (2,8). Find each of the following: (a) f(x,y) ds (Setup but do NOT evaluate) (b) f f(x,y) dy (Evaluate, should get 5408/15) (c) fc f(x, y) dx (Evaluate, should get 824/21) 2. Let F = (x² + 2y², x² + 2y²) and C be the same curve as in number 1. Find [ F Then show this is the same as 1b+1c and explain why. F · dr.
Transcribed Image Text:1. Let f(x, y) = x² + 2y² and C be the curve along y = r³ from (0, 0) to (2,8). Find each of the following: (a) f(x,y) ds (Setup but do NOT evaluate) (b) f f(x,y) dy (Evaluate, should get 5408/15) (c) fc f(x, y) dx (Evaluate, should get 824/21) 2. Let F = (x² + 2y², x² + 2y²) and C be the same curve as in number 1. Find [ F Then show this is the same as 1b+1c and explain why. F · dr.
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