Needed correct solutionPlease solve 100 percent correct (6) Let W be the region in R³ inside x² + y² = 1 that is below z = 3-²-² and above√² + y². More precisely,z = VW = {(x, y, z): x² + y² ≤ 1, √√² + y² ≤ x ≤3-2²-y²}.(a) Sketch the region W.(b) Consider a fluid of constant density μ(x, y, z) - 5 (measured in g/in³) flowing with velocityv(x, y, z) = (3ry² - e², y³ – x cos(2), z³ - y³)measured in in/s. Use the appropriate version of Stokes theorem to find the total amount of fluid (ingrams) that crosses the boundary of W flowing in the inward direction after 2 seconds.(c) What was the sign in your answer and what is the physical interpretation for this sign?

Answered: Image /qna-images/answer/0af2ea02-51dc-42b6-8cdd-cc1cf9edfb96.jpg

(6) Let W be the region in R³ inside x² + y² = 1 that is below z = 3-²-² and above √² + y². More precisely, z = V W = {(x, y, z): x² + y² ≤ 1, √√² + y² ≤ x ≤3-2²-y²}. (a) Sketch the region W. (b) Consider a fluid of constant density u(x, y, z) - 5 (measured in g/in³) flowing with velocity v(x, y, z) = (3xy² - e², y³ – x cos(2), z³ - y²) measured in in/s. Use the appropriate version of Stokes theorem to find the total amount of fluid (in the boundary of W flowing in the inward direction after 2 seconds.

(6) Let W be the region in R³ inside x² + y² = 1 that is below z = 3-²-² and above √² + y². More precisely, z = V W = {(x, y, z): x² + y² ≤ 1, √√² + y² ≤ x ≤3-2²-y²}. (a) Sketch the region W. (b) Consider a fluid of constant density u(x, y, z) - 5 (measured in g/in³) flowing with velocity v(x, y, z) = (3xy² - e², y³ – x cos(2), z³ - y²) measured in in/s. Use the appropriate version of Stokes theorem to find the total amount of fluid (in the boundary of W flowing in the inward direction after 2 seconds.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 11E

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