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Evaluate: $3y² dx + 2xydy using two different methods. C is the boundary of the graphs y = x2 from (3,9) to (0, 0) followed by the line segment from (0, 0) to (3, 9).

Evaluate: $3y² dx + 2xydy using two different methods. C is the boundary of the graphs y = x2 from (3,9) to (0, 0) followed by the line segment from (0, 0) to (3, 9).

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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**Problem 1:** Evaluate the line integral \(\oint_C 3y^2 \, dx + 2xy \, dy\) using two different methods. **Details:** - \(C\) is the boundary of the graphs: - \(y = x^2\) from \((3, 9)\) to \((0, 0)\) - Followed by the line segment from \((0, 0)\) to \((3, 9)\). This problem involves calculating the line integral of a vector field around a closed curve \(C\), using two different approaches. The path \(C\) is defined in two parts, first along the parabola \(y = x^2\) and then along a straight line.
Transcribed Image Text:**Problem 1:** Evaluate the line integral \(\oint_C 3y^2 \, dx + 2xy \, dy\) using two different methods. **Details:** - \(C\) is the boundary of the graphs: - \(y = x^2\) from \((3, 9)\) to \((0, 0)\) - Followed by the line segment from \((0, 0)\) to \((3, 9)\). This problem involves calculating the line integral of a vector field around a closed curve \(C\), using two different approaches. The path \(C\) is defined in two parts, first along the parabola \(y = x^2\) and then along a straight line.
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