Evaluate JJJB (z sin(x) + y² )dV 1 B = {(x, y, z) |— — — n ≤ x ≤ 1/2 T, 3 ≤ y ≤ 9,3 ≤ z ≤ 8} . 3 Round your answer to 4 decimal places.
Evaluate JJJB (z sin(x) + y² )dV 1 B = {(x, y, z) |— — — n ≤ x ≤ 1/2 T, 3 ≤ y ≤ 9,3 ≤ z ≤ 8} . 3 Round your answer to 4 decimal places.
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
5.4.10
![### Evaluating a Triple Integral
**Problem Statement:**
Evaluate the triple integral:
\[
\iiint_B (z \sin(x) + y^2) \, dV
\]
where the region \(B\) is defined as:
\[
B = \{ (x, y, z) \mid -\frac{1}{3}\pi \leq x \leq \frac{1}{2} \pi, \, 3 \leq y \leq 9, \, 3 \leq z \leq 8 \}
\]
**Instructions:**
- **Objective:** Compute the value of the integral over the specified region.
- **Output:** Round your answer to 4 decimal places.
**Exploration of Variables:**
- The variable \(x\) is bounded between \(-\frac{1}{3}\pi\) and \(\frac{1}{2}\pi\).
- The variable \(y\) ranges from 3 to 9.
- The variable \(z\) ranges from 3 to 8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F876c9bbd-0074-4123-babe-119feafc9f73%2Fa8bf09fa-3d51-4324-b51f-e90258b4fa2e%2Flrwok6l_processed.png&w=3840&q=75)
Transcribed Image Text:### Evaluating a Triple Integral
**Problem Statement:**
Evaluate the triple integral:
\[
\iiint_B (z \sin(x) + y^2) \, dV
\]
where the region \(B\) is defined as:
\[
B = \{ (x, y, z) \mid -\frac{1}{3}\pi \leq x \leq \frac{1}{2} \pi, \, 3 \leq y \leq 9, \, 3 \leq z \leq 8 \}
\]
**Instructions:**
- **Objective:** Compute the value of the integral over the specified region.
- **Output:** Round your answer to 4 decimal places.
**Exploration of Variables:**
- The variable \(x\) is bounded between \(-\frac{1}{3}\pi\) and \(\frac{1}{2}\pi\).
- The variable \(y\) ranges from 3 to 9.
- The variable \(z\) ranges from 3 to 8.
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