Use cylindrical coordinates to calculate the triple integral w f(x, y, z) dV for the function f(x, y, z) = 1936 Z the region x² + y² ≤ z ≤ 44 − (x² + y²). (Express numbers in exact form. Use symbolic notation and fractions where needed.) Incorrect f(x, y, z) dV = 781 √11 z 105√2 + and
Use cylindrical coordinates to calculate the triple integral w f(x, y, z) dV for the function f(x, y, z) = 1936 Z the region x² + y² ≤ z ≤ 44 − (x² + y²). (Express numbers in exact form. Use symbolic notation and fractions where needed.) Incorrect f(x, y, z) dV = 781 √11 z 105√2 + and
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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Question
![### Problem Statement
Use cylindrical coordinates to calculate the triple integral
\[
\iiint_W f(x, y, z) \, dV
\]
for the function
\[
f(x, y, z) = \frac{1}{1936} z \sqrt{x^2 + y^2}
\]
and the region
\[
x^2 + y^2 \leq z \leq 44 - (x^2 + y^2).
\]
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
### Attempted Solution
The attempted solution for the triple integral is presented as:
\[
\iiint_W f(x, y, z) \, dV = \frac{781 \sqrt{11 \pi}}{105 \sqrt{2}}
\]
**Note:** The solution given is marked as incorrect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1f44d6-2912-49cf-894d-a588f3241dc5%2Fbc7b50c3-d392-49c8-9acd-2c2f489f730b%2Fb9rn0o_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Use cylindrical coordinates to calculate the triple integral
\[
\iiint_W f(x, y, z) \, dV
\]
for the function
\[
f(x, y, z) = \frac{1}{1936} z \sqrt{x^2 + y^2}
\]
and the region
\[
x^2 + y^2 \leq z \leq 44 - (x^2 + y^2).
\]
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
### Attempted Solution
The attempted solution for the triple integral is presented as:
\[
\iiint_W f(x, y, z) \, dV = \frac{781 \sqrt{11 \pi}}{105 \sqrt{2}}
\]
**Note:** The solution given is marked as incorrect.
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