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F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b) the Fundamental Theorem of Line Integrals.

F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b) the 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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**Problem 3: Vector Field Integration** Given the vector field \( \mathbf{F}(x, y) = \langle 4x^3, 3y^2 \rangle \), find the line integral \(\int \mathbf{F} \cdot d\mathbf{r} \) along a path from the point \((0, 0)\) to \((2, 6)\). Consider two methods for solving the problem: a) **Using a Parabolic Path** b) **Using the Fundamental Theorem of Line Integrals**
Transcribed Image Text:**Problem 3: Vector Field Integration** Given the vector field \( \mathbf{F}(x, y) = \langle 4x^3, 3y^2 \rangle \), find the line integral \(\int \mathbf{F} \cdot d\mathbf{r} \) along a path from the point \((0, 0)\) to \((2, 6)\). Consider two methods for solving the problem: a) **Using a Parabolic Path** b) **Using the Fundamental Theorem of Line Integrals**
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