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Let F = (P(x, y), Q(x, y)) = (xy, x + y) and let C be the circle x² + y² = 4, oriented counterclockwise (as above). Find the circulation of around C by using Green's theorem. In this case, Q = = and Py Thus the circulation of Faround C = = JS₁ 2 x² + y² = 4. Evaluating this, the circulation of Faround C is dA, where R is the region bounded by

Let F = (P(x, y), Q(x, y)) = (xy, x + y) and let C be the circle x² + y² = 4, oriented counterclockwise (as above). Find the circulation of around C by using Green's theorem. In this case, Q = = and Py Thus the circulation of Faround C = = JS₁ 2 x² + y² = 4. Evaluating this, the circulation of Faround C is dA, where R is the region bounded by

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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Let \(\vec{F} = \langle P(x, y), Q(x, y) \rangle = \langle xy, x + y \rangle\) and let \(C\) be the circle \(x^2 + y^2 = 4\), oriented counterclockwise (as above). Find the circulation of \(\vec{F}\) around \(C\) by using Green's theorem. In this case, \(Q_x = \underline{\hspace{1cm}}\) and \(P_y = \underline{\hspace{1cm}}\). Thus the circulation of \(\vec{F}\) around \(C = \iint_R \underline{\hspace{2cm}} \, dA\), where \(R\) is the region bounded by \(x^2 + y^2 = 4\). Evaluating this, the circulation of \(\vec{F}\) around \(C\) is \(\underline{\hspace{1cm}}\).
Transcribed Image Text:Let \(\vec{F} = \langle P(x, y), Q(x, y) \rangle = \langle xy, x + y \rangle\) and let \(C\) be the circle \(x^2 + y^2 = 4\), oriented counterclockwise (as above). Find the circulation of \(\vec{F}\) around \(C\) by using Green's theorem. In this case, \(Q_x = \underline{\hspace{1cm}}\) and \(P_y = \underline{\hspace{1cm}}\). Thus the circulation of \(\vec{F}\) around \(C = \iint_R \underline{\hspace{2cm}} \, dA\), where \(R\) is the region bounded by \(x^2 + y^2 = 4\). Evaluating this, the circulation of \(\vec{F}\) around \(C\) is \(\underline{\hspace{1cm}}\).
Let \( \vec{F} = \langle xy, x + y \rangle \) and let \( C \) be the circle \( x^2 + y^2 = 4 \), oriented counterclockwise. Find the circulation of \( \vec{F} \) around \( C \) by computing \( \oint_C \vec{F} \cdot d\vec{r} \). [Textbox for answer input]
Transcribed Image Text:Let \( \vec{F} = \langle xy, x + y \rangle \) and let \( C \) be the circle \( x^2 + y^2 = 4 \), oriented counterclockwise. Find the circulation of \( \vec{F} \) around \( C \) by computing \( \oint_C \vec{F} \cdot d\vec{r} \). [Textbox for answer input]
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