Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary ofthe semi annular region D in the upper half-plane between the circles x² + y² = 1and x² + y² = 4.Q8. Evaluate F. dr using Stoke's theorem when F = (2xy - x²)ī —(x² - y² )j and C is the boundary of the region enclosed by the parabolas y² = xand x² = y.Q9. Find the value of the right side of Gauss divergence theorem for F = x²ī+ zī+yz k over the cube formed by x = +1, y = ±1, z = +1.

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Answered: Q7. Use Green's theorem to evaluate 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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Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular region D in the upper half-plane between the circles x² + y² = 1 and x² + y² = 4.