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Use the Green's Theorem to evaluate the line integral f, FdT where F = (sin(x²)-2x²y) i+ (cos(y?) + x³) i and L is a closed curve that consists of a part of the parabola y = x2 and the line y = 1, with –1 < x <1 oriented counterclockwise. 6.

Use the Green's Theorem to evaluate the line integral f, FdT where F = (sin(x²)-2x²y) i+ (cos(y?) + x³) i and L is a closed curve that consists of a part of the parabola y = x2 and the line y = 1, with –1 < x <1 oriented counterclockwise. 6.

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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6. Use Green's Theorem to evaluate the line integral \(\int_L \vec{F} \cdot d\vec{r}\) where \(\vec{F} = (\sin(x^2) - 2x^2 y) \vec{i} + (\cos(y^2) + x^3) \vec{j}\) and \(L\) is a closed curve that consists of a part of the parabola \(y = x^2\) and the line \(y = 1\), with \(-1 \leq x \leq 1\), oriented counterclockwise.
Transcribed Image Text:6. Use Green's Theorem to evaluate the line integral \(\int_L \vec{F} \cdot d\vec{r}\) where \(\vec{F} = (\sin(x^2) - 2x^2 y) \vec{i} + (\cos(y^2) + x^3) \vec{j}\) and \(L\) is a closed curve that consists of a part of the parabola \(y = x^2\) and the line \(y = 1\), with \(-1 \leq x \leq 1\), oriented counterclockwise.
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