Let H be the hemisphere x2 + y2 + z2 = 29, z ≥ 0, and suppose f is a continuous function with f(3, 2, 4) = 7, f(3, −2, 4) = 8, f(−3, 2, 4) = 10, and f(−3, −2, 4) = 12. By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.) Hf(x, y, z) dS
Let H be the hemisphere x2 + y2 + z2 = 29, z ≥ 0, and suppose f is a continuous function with f(3, 2, 4) = 7, f(3, −2, 4) = 8, f(−3, 2, 4) = 10, and f(−3, −2, 4) = 12. By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.) Hf(x, y, z) dS
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Let H be the hemisphere
x2 + y2 + z2 = 29, z ≥ 0,
and suppose f is a continuous function with
f(3, 2, 4) = 7,
f(3, −2, 4) = 8,
f(−3, 2, 4) = 10,
and
f(−3, −2, 4) = 12.
By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.)| H |
![Let \( H \) be the hemisphere \( x^2 + y^2 + z^2 = 29, \, z \geq 0 \), and suppose \( f \) is a continuous function with \( f(3, 2, 4) = 7 \), \( f(3, -2, 4) = 8 \), \( f(-3, 2, 4) = 10 \), and \( f(-3, -2, 4) = 12 \). By dividing \( H \) into four patches, estimate the value below. (Round your answer to the nearest whole number.)
\[
\iint_H f(x, y, z) \, dS
\]
\_\_\_\_\_\_\_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a03be36-5dfa-4a37-af0e-f31c338c2b5f%2F9c0de1ac-09b7-4b04-a57c-7c613181dcbf%2Fvqg4fp_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( H \) be the hemisphere \( x^2 + y^2 + z^2 = 29, \, z \geq 0 \), and suppose \( f \) is a continuous function with \( f(3, 2, 4) = 7 \), \( f(3, -2, 4) = 8 \), \( f(-3, 2, 4) = 10 \), and \( f(-3, -2, 4) = 12 \). By dividing \( H \) into four patches, estimate the value below. (Round your answer to the nearest whole number.)
\[
\iint_H f(x, y, z) \, dS
\]
\_\_\_\_\_\_\_
Expert Solution
Step 1
The equation of a sphere is represented as: , where r is the radius of the sphere.
It is known that: .
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