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Find the value of the triple integral for w= x bounded by: x² + y² ≤ z≤ 4 and x² + y² = 4 in the xy-plane.

Find the value of the triple integral for w= x bounded by: x² + y² ≤ z≤ 4 and x² + y² = 4 in the xy-plane.

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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**3.** Find the value of the triple integral for \( w = 4z \) bounded by: \( 0 \leq z \leq \sqrt{x^2 + y^2} \) and \( x^2 + y^2 = 9 \) in the \( xy \)-plane. **4.** Find 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.** Find the value of the triple integral for \( w = \sin(y^2) \) bounded by \( x = 0 \), \( x = y \), \( y = 0 \), \( y = \frac{\sqrt{\pi}}{2} \), \( z = 1 \) and \( z = 3 \).
Transcribed Image Text:**3.** Find the value of the triple integral for \( w = 4z \) bounded by: \( 0 \leq z \leq \sqrt{x^2 + y^2} \) and \( x^2 + y^2 = 9 \) in the \( xy \)-plane. **4.** Find 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.** Find the value of the triple integral for \( w = \sin(y^2) \) bounded by \( x = 0 \), \( x = y \), \( y = 0 \), \( y = \frac{\sqrt{\pi}}{2} \), \( z = 1 \) and \( z = 3 \).
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