Evaluate √√x² + y² dA, where D is the domain in the figure and a = 10. -X (Give your answer in exact form. Use symbolic notation and fractions where needed.) Hint: Find the equation of the inner circle in polar coordinates and treat the right and left parts of the region separately. D₁₂√x² + 3² dA=
Evaluate √√x² + y² dA, where D is the domain in the figure and a = 10. -X (Give your answer in exact form. Use symbolic notation and fractions where needed.) Hint: Find the equation of the inner circle in polar coordinates and treat the right and left parts of the region separately. D₁₂√x² + 3² dA=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Evaluate**
\[ \iint_{D} \sqrt{x^2 + y^2} \, dA, \]
where \( D \) is the domain in the figure and \( a = 10 \).
---
### Diagram Explanation
The diagram shows two concentric circles on a Cartesian plane:
- **Outer Circle:**
- Centered at the origin.
- Larger circle with radius \( a = 10 \).
- **Inner Circle:**
- Centered on the positive x-axis, split equally between left and right around the point \(\left(\frac{a}{2}, 0\right)\).
- Smaller circle with radius \(\frac{a}{2} = 5\).
Both circles are displayed in blue with the region between them shaded in beige.
### Instructions
- **Answer in Exact Form:** Use symbolic notation and fractions where necessary.
### Hint
- Find the equation of the inner circle in polar coordinates.
- Treat the right and left parts of the region separately.
\[
\iint_{D} \sqrt{x^2 + y^2} \, dA = \boxed{\phantom{\text{Insert Answer Here}}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1f44d6-2912-49cf-894d-a588f3241dc5%2F05d4e070-56b9-4b9b-9e97-23115574df41%2F4h872v_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate**
\[ \iint_{D} \sqrt{x^2 + y^2} \, dA, \]
where \( D \) is the domain in the figure and \( a = 10 \).
---
### Diagram Explanation
The diagram shows two concentric circles on a Cartesian plane:
- **Outer Circle:**
- Centered at the origin.
- Larger circle with radius \( a = 10 \).
- **Inner Circle:**
- Centered on the positive x-axis, split equally between left and right around the point \(\left(\frac{a}{2}, 0\right)\).
- Smaller circle with radius \(\frac{a}{2} = 5\).
Both circles are displayed in blue with the region between them shaded in beige.
### Instructions
- **Answer in Exact Form:** Use symbolic notation and fractions where necessary.
### Hint
- Find the equation of the inner circle in polar coordinates.
- Treat the right and left parts of the region separately.
\[
\iint_{D} \sqrt{x^2 + y^2} \, dA = \boxed{\phantom{\text{Insert Answer Here}}}
\]
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