Show the integral as follows: (A+2x) ! Vl-x (x²+y®) 21.xy'dzdydx -VI-x -(x²+y°) Calculation:
Show the integral as follows: (A+2x) ! Vl-x (x²+y®) 21.xy'dzdydx -VI-x -(x²+y°) Calculation:
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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For the problem in attached image, find the
How do I determine the range of Theta?
![**Given Information:**
Show the integral as follows:
\[
\int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} \int_{-(x^2+y^2)}^{(x^2+y^2)} 21xy^2 \, dz \, dy \, dx
\]
**Calculation:**
Show the relation as follows:
\[
x = r \cos \theta
\]
\[
y = r \sin \theta
\]
\[
z = z
\]
\[
(x^2 + y^2) = r^2
\]
Show the relation as follows:
\[
(x^2 + y^2) = 1
\]
\[
(r \cos \theta)^2 + (r \sin \theta)^2 = 1
\]
\[
r^2 (\cos^2 \theta + \sin^2 \theta) = 1
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ff4c54b-33c6-4611-b43d-db7328cbccac%2Faa7029b1-8b20-403b-b4c8-ef8e30a45fdb%2F8xuvlc4v_processed.png&w=3840&q=75)
Transcribed Image Text:**Given Information:**
Show the integral as follows:
\[
\int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} \int_{-(x^2+y^2)}^{(x^2+y^2)} 21xy^2 \, dz \, dy \, dx
\]
**Calculation:**
Show the relation as follows:
\[
x = r \cos \theta
\]
\[
y = r \sin \theta
\]
\[
z = z
\]
\[
(x^2 + y^2) = r^2
\]
Show the relation as follows:
\[
(x^2 + y^2) = 1
\]
\[
(r \cos \theta)^2 + (r \sin \theta)^2 = 1
\]
\[
r^2 (\cos^2 \theta + \sin^2 \theta) = 1
\]
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