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Let B be the solid bounded by the cylinder x² + y² = 9 and the planes z = 0 and z = 2. Let F be the vector field F(x, y, z) = (x, y, (4 − z²)(x² + y²) Jon FdS, where OB is the three-sided boundary of B, oriented with outward-pointing normal vectors. dB 1. Calculate the flux integral 2. Let f(x, y, z) = V · F= 2 − 2z(x² + y²). Calculate the triple integral off over the solid region B. You should get the same answer! What is it? Give an exact answer: хл

Let B be the solid bounded by the cylinder x² + y² = 9 and the planes z = 0 and z = 2. Let F be the vector field F(x, y, z) = (x, y, (4 − z²)(x² + y²) Jon FdS, where OB is the three-sided boundary of B, oriented with outward-pointing normal vectors. dB 1. Calculate the flux integral 2. Let f(x, y, z) = V · F= 2 − 2z(x² + y²). Calculate the triple integral off over the solid region B. You should get the same answer! What is it? Give an exact answer: хл

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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can you please show me what formula is used to solve this and how to identify what type of integral this is as well as knowing what method to use when approaching this type of problem. 

Let B be the solid bounded by the cylinder x² + y² = 9 and the planes z = 0 and z = 2. Let F be the vector field F(x, y, z) = (x, y, (4 — z²)(x² + y²)). 1. Calculate the flux integral FdS, where dB is the three-sided boundary of B, oriented with outward-pointing normal vectors. дв 2. Let ƒ(x, y, z) = V · F= 2 − 2z(x² + y²). Calculate the triple integral of f over the solid region B. You should get the same answer! What is it? Give an exact answer: The correct answer is: -126 хл
Transcribed Image Text:Let B be the solid bounded by the cylinder x² + y² = 9 and the planes z = 0 and z = 2. Let F be the vector field F(x, y, z) = (x, y, (4 — z²)(x² + y²)). 1. Calculate the flux integral FdS, where dB is the three-sided boundary of B, oriented with outward-pointing normal vectors. дв 2. Let ƒ(x, y, z) = V · F= 2 − 2z(x² + y²). Calculate the triple integral of f over the solid region B. You should get the same answer! What is it? Give an exact answer: The correct answer is: -126 хл
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