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30 Evaluate .P S: с Tw ds (w=J²) J along a) ONP (b) OBP

30 Evaluate .P S: с Tw ds (w=J²) J along a) ONP (b) OBP

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 Statement Evaluate the integral \(\oint \sigma W \, ds\) along the paths: a) ONP b) OBP ### Diagram Explanation The diagram is a graph plotted on the complex plane with axes labeled \(\sigma\) (real axis) and \(j\omega\) (imaginary axis). It shows a contour labeled as \(C\) where \(W = \sigma^2\). #### Key Points in the Graph: - **O:** The origin point. - **N:** A point along the curved path ONP. - **B:** A point on the real axis directly below point P. - **P:** A point in the complex plane where the contour \(C\) intersects. - **Path ONP:** A curved path beginning at O, going through N, and ending at P. - **Path OBP:** A path from O to B along the \(\sigma\) axis, then vertically to P. The contour \(C\) is indicated by a path where \(\omega = \sigma^2\). ### Task Evaluate the given integral along the specified paths using the shown contour.
Transcribed Image Text:### Problem Statement Evaluate the integral \(\oint \sigma W \, ds\) along the paths: a) ONP b) OBP ### Diagram Explanation The diagram is a graph plotted on the complex plane with axes labeled \(\sigma\) (real axis) and \(j\omega\) (imaginary axis). It shows a contour labeled as \(C\) where \(W = \sigma^2\). #### Key Points in the Graph: - **O:** The origin point. - **N:** A point along the curved path ONP. - **B:** A point on the real axis directly below point P. - **P:** A point in the complex plane where the contour \(C\) intersects. - **Path ONP:** A curved path beginning at O, going through N, and ending at P. - **Path OBP:** A path from O to B along the \(\sigma\) axis, then vertically to P. The contour \(C\) is indicated by a path where \(\omega = \sigma^2\). ### Task Evaluate the given integral along the specified paths using the shown contour.
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