Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. S F(x, y, z) = yi-xj + 4zk, S is the hemisphere x2 + y2 +z² = 4, z≥ 0, oriented downward x Need Help? Read It

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
icon
Related questions
Question
Evaluate the surface integral
F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
S
F(x, y, z) = yi-xj + 4zk, S is the hemisphere x2 + y2 +z² = 4, z≥ 0, oriented downward
x
Need Help?
Read It
Transcribed Image Text:Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. S F(x, y, z) = yi-xj + 4zk, S is the hemisphere x2 + y2 +z² = 4, z≥ 0, oriented downward x Need Help? Read It
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage