3. Evaluate: $(x³ + xy) dx + [x² − ln(y²)]dy using one method. C is the boundary of a region bounded by the graphs of circles with radii of 2 and 4 centered at the origin oriented counterclockwise.
3. Evaluate: $(x³ + xy) dx + [x² − ln(y²)]dy using one method. C is the boundary of a region bounded by the graphs of circles with radii of 2 and 4 centered at the origin oriented counterclockwise.
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
![**Problem 2:**
Evaluate the line integral:
\[
\oint_C (8y - x^2) \, dx + [2x - 3y^2 + y]\, dy
\]
using one method. Here, \( C \) is the boundary of the graph of a circle of radius 4 oriented counterclockwise.
**Problem 3:**
Evaluate the line integral:
\[
\oint_C (x^3 + xy) \, dx + [x^2 - \ln(y^2)] \, dy
\]
using one method. Here, \( C \) is the boundary of a region bounded by the graphs of circles with radii of 2 and 4 centered at the origin, oriented counterclockwise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca92bf5f-8e35-4ea7-bd85-d600dcb720b2%2F8d7d6881-607a-4a10-a53e-a505124f73ac%2Frts4ksq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2:**
Evaluate the line integral:
\[
\oint_C (8y - x^2) \, dx + [2x - 3y^2 + y]\, dy
\]
using one method. Here, \( C \) is the boundary of the graph of a circle of radius 4 oriented counterclockwise.
**Problem 3:**
Evaluate the line integral:
\[
\oint_C (x^3 + xy) \, dx + [x^2 - \ln(y^2)] \, dy
\]
using one method. Here, \( C \) is the boundary of a region bounded by the graphs of circles with radii of 2 and 4 centered at the origin, oriented counterclockwise.
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