3. Find the value of the triple integral for w = 4z bounded by: 0 ≤ z≤ √√x² + y² and x² + y² = 9 in the xy-plane. 4. Find the value of the triple integral for w = x bounded by: x² + y² ≤ z ≤ 4 and x² + y² = 4 in the xy-plane. 5. Find the value of the triple integral for w = sin (y²) bounded by x = 0, x = y, y = 0, y = z = 1 and z= 3.
3. Find the value of the triple integral for w = 4z bounded by: 0 ≤ z≤ √√x² + y² and x² + y² = 9 in the xy-plane. 4. Find the value of the triple integral for w = x bounded by: x² + y² ≤ z ≤ 4 and x² + y² = 4 in the xy-plane. 5. Find the value of the triple integral for w = sin (y²) bounded by x = 0, x = y, y = 0, y = z = 1 and z= 3.
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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I need help with #3
![**Triple Integral Problems**
3. Determine the value of the triple integral for \( w = 4z \) bounded by the region:
\[
0 \leq z \leq \sqrt{x^2 + y^2}
\]
and
\[
x^2 + y^2 = 9
\]
in the \( xy \)-plane.
4. Calculate the value of the triple integral for \( w = x \) bounded by:
\[
x^2 + y^2 \leq z \leq 4
\]
and
\[
x^2 + y^2 = 4
\]
in the \( xy \)-plane.
5. Evaluate the value of the triple integral for \( w = \sin(y^2) \) bounded by:
\[
x = 0, \quad x = y, \quad y = 0, \quad y = \frac{\pi}{2}
\]
along with
\[
z = 1 \quad \text{and} \quad z = 3.
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Transcribed Image Text:**Triple Integral Problems**
3. Determine the value of the triple integral for \( w = 4z \) bounded by the region:
\[
0 \leq z \leq \sqrt{x^2 + y^2}
\]
and
\[
x^2 + y^2 = 9
\]
in the \( xy \)-plane.
4. Calculate the value of the triple integral for \( w = x \) bounded by:
\[
x^2 + y^2 \leq z \leq 4
\]
and
\[
x^2 + y^2 = 4
\]
in the \( xy \)-plane.
5. Evaluate the value of the triple integral for \( w = \sin(y^2) \) bounded by:
\[
x = 0, \quad x = y, \quad y = 0, \quad y = \frac{\pi}{2}
\]
along with
\[
z = 1 \quad \text{and} \quad z = 3.
\]
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