Evaluate the triple integral I = = ≥ 0, y ≥ 0, z ≥ 0. A. I = ㅠ 20 B. I = T15 C. I = 0 E. I = 15 77 D. I = 15 10 π 40 =(2²+3²) dV where D is the region inside the cone z = D 15 x² + y2, below the plane z = 1 and inside the first octant
Evaluate the triple integral I = = ≥ 0, y ≥ 0, z ≥ 0. A. I = ㅠ 20 B. I = T15 C. I = 0 E. I = 15 77 D. I = 15 10 π 40 =(2²+3²) dV where D is the region inside the cone z = D 15 x² + y2, below the plane z = 1 and inside the first octant
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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![**Problem Statement:**
Evaluate the triple integral
\[
I = \iiint_D (x^2 + y^2) \, dV
\]
where \( D \) is the region inside the cone \( z = \sqrt{x^2 + y^2} \), below the plane \( z = 1 \), and inside the first octant \( x \geq 0 \), \( y \geq 0 \), \( z \geq 0 \).
**Options:**
A. \( I = \frac{\pi}{20} \)
B. \( I = \pi \)
C. \( I = 0 \)
D. \( I = \frac{\pi}{10} \)
E. \( I = \frac{\pi}{40} \)
**Correct Answer:**
Option D is selected: \( I = \frac{\pi}{10} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39ee3059-6733-456c-bbc4-46bedd3c18f2%2F1c42ae1a-5f12-402f-a011-422c6eb5807e%2Fa8x6nvd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Evaluate the triple integral
\[
I = \iiint_D (x^2 + y^2) \, dV
\]
where \( D \) is the region inside the cone \( z = \sqrt{x^2 + y^2} \), below the plane \( z = 1 \), and inside the first octant \( x \geq 0 \), \( y \geq 0 \), \( z \geq 0 \).
**Options:**
A. \( I = \frac{\pi}{20} \)
B. \( I = \pi \)
C. \( I = 0 \)
D. \( I = \frac{\pi}{10} \)
E. \( I = \frac{\pi}{40} \)
**Correct Answer:**
Option D is selected: \( I = \frac{\pi}{10} \).
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