for the first image attach please do the calculations similar to the second image attachplease please answer every correctly also this is not a graded question I would really appreciate if you would answer [15] (4) GIVEN: a > 0, a constant, and thedirected path C,from A = (a,0) to B= (0, a),directed along the line segment, AB;Add extrapages, asneeded.and, the vector field in the xy - plane,(x² − y², x² + y²).FFIND: The path integral: F•ds=6 771A(a,0) /117F = (x² − y², x² + y²)111A 11X [15] (4)GIVEN: a > 0, a constant, and thedirected path c,from A = (a,0) to B= (a, a) to C = (0,0),directed along the line segments, AB, BC;and, the vector field in the xy - plane,F = (x + y, - x).FIND: The path integral: F·dsMETHOD:1AB: C = (a,y), ye [o,a]BC: -C₂ = (x,x), z€ [0,a]diF•=Lên đã đến đâện đã-C₂.Lên đã = f(a+y, a)(0,1)= √² (-a) dy = − a²Hence,(a,0)F = (x+y₁-x)·ad√ F• dî = [ª (2x,-z). (1,1) 4 = √x+-C₂= 1/α²√ F• dª = -a² - £a² = −2a²The negativevalue of the answer,(checks with the sketch.

Answered: Image /qna-images/answer/3c6c6bd4-6053-421b-ae71-45b633229c68.jpg

[15] (4) GIVEN: a > 0, a constant, and the directed path C, (Add extra pages, as needed. from A = (a,0) to B= (0, a), directed along the line segment, AB; and, the vector field in the xy - plane, F = (x² - y², x² + y²). FIND: The path integral: F•ds (0, a) / 1 1 ΚΑ (a,0) / X 1 1 1 F = (x² − y², x² + y²)

[15] (4) GIVEN: a > 0, a constant, and the directed path C, (Add extra pages, as needed. from A = (a,0) to B= (0, a), directed along the line segment, AB; and, the vector field in the xy - plane, F = (x² - y², x² + y²). FIND: The path integral: F•ds (0, a) / 1 1 ΚΑ (a,0) / X 1 1 1 F = (x² − y², x² + y²)

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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