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Evaluate: fydx + xdy along a path from (0, 0) to (2, 4) by finding r(t) that matches t following graphs. a) + b) + c) Evaluate by using Fundamental Theorem of Line Integrals.

Evaluate: fydx + xdy along a path from (0, 0) to (2, 4) by finding r(t) that matches t following graphs. a) + b) + c) Evaluate by using Fundamental Theorem of Line Integrals.

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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I need help with #5
**Problem 5: Line Integral Evaluation** Evaluate the line integral \( \int y \, dx + x \, dy \) along a path from the point (0, 0) to (2, 4) by finding a vector function \(\vec{r}(t)\) that matches the graphs provided. **Graph Descriptions:** - **Graph a:** - The path starts at the origin (0, 0) and follows a curved trajectory upward and to the right, reaching the point (2, 4). - **Graph b:** - The path starts at the origin (0, 0) and proceeds directly along a straight line to reach the point (2, 4). **Part c:** - Evaluate the integral by using the Fundamental Theorem of Line Integrals. This instructs to determine and evaluate the line integral by using an appropriate vector function and to apply the theorem for simplified computation.
Transcribed Image Text:**Problem 5: Line Integral Evaluation** Evaluate the line integral \( \int y \, dx + x \, dy \) along a path from the point (0, 0) to (2, 4) by finding a vector function \(\vec{r}(t)\) that matches the graphs provided. **Graph Descriptions:** - **Graph a:** - The path starts at the origin (0, 0) and follows a curved trajectory upward and to the right, reaching the point (2, 4). - **Graph b:** - The path starts at the origin (0, 0) and proceeds directly along a straight line to reach the point (2, 4). **Part c:** - Evaluate the integral by using the Fundamental Theorem of Line Integrals. This instructs to determine and evaluate the line integral by using an appropriate vector function and to apply the theorem for simplified computation.
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