Sketch the region R and evaluate the iterated integral f(x, y) dA. 30 15 (x + y) dx dy 16 30 14
Sketch the region R and evaluate the iterated integral f(x, y) dA. 30 15 (x + y) dx dy 16 30 14
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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14.2 2
![**Transcription:**
Sketch the region \( R \) and evaluate the iterated integral
\[
\iint_R f(x, y) \, dA.
\]
\[
\int_0^{30} \int_{y/2}^{15} (x + y) \, dx \, dy
\]
**Explanation of Diagram:**
The image includes a coordinate plane with marked axes. Although the complete graphs or detailed diagrams are not visible, based on the integral limits given, the region \( R \) is defined by the bounds:
- The outer integral with respect to \( y \): \( y \) varies from 0 to 30.
- The inner integral with respect to \( x \): for a given \( y \), \( x \) varies from \( y/2 \) to 15.
To sketch this region, plot:
1. The line \( x = y/2 \).
2. The vertical line \( x = 15 \).
3. The horizontal lines \( y = 0 \) and \( y = 30 \).
The region \( R \) is bounded by these lines and forms a trapezoidal area in the coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2Fc2d57669-72d7-4163-bb2b-50359f805384%2Foon9wea_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription:**
Sketch the region \( R \) and evaluate the iterated integral
\[
\iint_R f(x, y) \, dA.
\]
\[
\int_0^{30} \int_{y/2}^{15} (x + y) \, dx \, dy
\]
**Explanation of Diagram:**
The image includes a coordinate plane with marked axes. Although the complete graphs or detailed diagrams are not visible, based on the integral limits given, the region \( R \) is defined by the bounds:
- The outer integral with respect to \( y \): \( y \) varies from 0 to 30.
- The inner integral with respect to \( x \): for a given \( y \), \( x \) varies from \( y/2 \) to 15.
To sketch this region, plot:
1. The line \( x = y/2 \).
2. The vertical line \( x = 15 \).
3. The horizontal lines \( y = 0 \) and \( y = 30 \).
The region \( R \) is bounded by these lines and forms a trapezoidal area in the coordinate plane.
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