Let S be the portion of the surface z = 1 - x^2 - y^2 that lies above the xy-plane, and suppose that S is oriented upwards. Find the flux of the vector field F(x, y, z) = xi + yj + zk across S.
Added by Gerald B.
Step 1
First, we need to parameterize the surface S. Since it lies above the xy-plane, we can use polar coordinates to parameterize it. Let x = r*cos(θ), y = r*sin(θ), z = 1 - r^2, where 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 83 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Problem #7: Find the flux of the vector field F = xi + e^(5x)j + zk through the surface S given by that portion of the plane 5x + y + 7z = 6 in the first octant, oriented upward.
Adi S.
The surface S is the hemisphere x 2 + y 2 + z 2 = 1, z ≥ 0 with upward orientation. Compute the flux of the vector field F(x, y, z) = y i − x j + 4z 2 k across S
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD