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11-14 Use Green's Theorem to evaluate e F. dr. (Check the orientation of the curve before applying the theorem.) CLA 11. F(x, y) = (y cos x - xy sinx, xy xy sin x. xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0) 12. F(x, y) = (ex + y²e + x²), C consists of the arc of the curve y == cos x from (-T/2, 0) to (π/2, 0) and the line segment from (7/2, 0) to (-T/2, 0) 13. F(x, y) = (y - cos y, x sin y), - C is the circle (x − 3)² + (y + 4)² = 4 oriented clockwise

11-14 Use Green's Theorem to evaluate e F. dr. (Check the orientation of the curve before applying the theorem.) CLA 11. F(x, y) = (y cos x - xy sinx, xy xy sin x. xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0) 12. F(x, y) = (ex + y²e + x²), C consists of the arc of the curve y == cos x from (-T/2, 0) to (π/2, 0) and the line segment from (7/2, 0) to (-T/2, 0) 13. F(x, y) = (y - cos y, x sin y), - C is the circle (x − 3)² + (y + 4)² = 4 oriented clockwise

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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is the rectangle with vertices (0, 0), (3, 0), (3, 4), and (0,4) 6. fc (x² + y²) dx + (x² - y²) dy, C is the triangle with vertices (0, 0), (2, 1), and (0, 1) 7. fc (y + e√) dx + (2x + cos y²) dy, C is the boundary of the region enclosed by the parabolas y = x² and x = y² 8. fcy¹ dx + 2xy³ dy, C is the ellipse x² + 2y² = 2 9. Scy³ dx - x³ dy, C is the circle x² + y² = 4 10. fc (1 - y³) dx + (x³ + ey²) dy, C is the boundary of the region between the circles x² + y² = 4 and x² + y² = 9 11-14 Use Green's Theorem to evaluate e F. dr. (Check the orientation of the curve before applying the theorem.) 300 11. F(x, y) = (y cos x xy sinx, xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0) 12. F(x, y) = (ex + y², e³ + x²), C consists of the arc of the curve y cos x from (-π/2, 0) to (π/2, 0) and the line segment from (7/2, 0) to (-T/2, 0) 11 13. F(x, y) = (y - cos y, x sin y), C is the circle (x − 3)² + (y + 4)² = 4 oriented clockwise 14. F(x, y) = (√x² + 1, tan¯¹x), C is the triangle from (0, 0) to (1, 1) to (0, 1) to (0, 0) CAS 15-16 Verify Green's Theorem by using a computer algebra system to evaluate both the line integral and the double integral. 15. P(x, y) = x³y4, Q(x, y) = x³y4, C consists of the line segment from (-7/2, 0) to (π/2, 0) followed by the arc of the curve y = cos x from (π/2, 0) to (-TT/2, 0) 16. P(x, y) = 2x - x³y³, Q(x, y) = x³y8, C is the ellipse 4x² + y² = 4 17. Use Green's Theorem to find the work done by the force F(x, y) = x(x + y) i + xy² j in moving a particle from the origin along the x-axis to (1, 0), then along the line to (0, 1), and then back to the origin along the y-axis. segment cycloid and us 21. (a) If C is the the point ( S (b) If the verti are (x₁, y₁. the polygo A = 1/[(x₁ (c) Find the a (1, 3), (0, 22. Let D be a reg xy-plane. Use nates of the ce 1 2A where A is the x = 23. Use Exercise region of radi 24. Use Exercise vertices (0, 0) 25. A plane lamin region in the Show that its Ix = - 26. Use Exercise disk of radius (Compare wit 27. Use the metho F and C is any E encloses the c 28. Calculate fe F C is the SILI
Transcribed Image Text:is the rectangle with vertices (0, 0), (3, 0), (3, 4), and (0,4) 6. fc (x² + y²) dx + (x² - y²) dy, C is the triangle with vertices (0, 0), (2, 1), and (0, 1) 7. fc (y + e√) dx + (2x + cos y²) dy, C is the boundary of the region enclosed by the parabolas y = x² and x = y² 8. fcy¹ dx + 2xy³ dy, C is the ellipse x² + 2y² = 2 9. Scy³ dx - x³ dy, C is the circle x² + y² = 4 10. fc (1 - y³) dx + (x³ + ey²) dy, C is the boundary of the region between the circles x² + y² = 4 and x² + y² = 9 11-14 Use Green's Theorem to evaluate e F. dr. (Check the orientation of the curve before applying the theorem.) 300 11. F(x, y) = (y cos x xy sinx, xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0) 12. F(x, y) = (ex + y², e³ + x²), C consists of the arc of the curve y cos x from (-π/2, 0) to (π/2, 0) and the line segment from (7/2, 0) to (-T/2, 0) 11 13. F(x, y) = (y - cos y, x sin y), C is the circle (x − 3)² + (y + 4)² = 4 oriented clockwise 14. F(x, y) = (√x² + 1, tan¯¹x), C is the triangle from (0, 0) to (1, 1) to (0, 1) to (0, 0) CAS 15-16 Verify Green's Theorem by using a computer algebra system to evaluate both the line integral and the double integral. 15. P(x, y) = x³y4, Q(x, y) = x³y4, C consists of the line segment from (-7/2, 0) to (π/2, 0) followed by the arc of the curve y = cos x from (π/2, 0) to (-TT/2, 0) 16. P(x, y) = 2x - x³y³, Q(x, y) = x³y8, C is the ellipse 4x² + y² = 4 17. Use Green's Theorem to find the work done by the force F(x, y) = x(x + y) i + xy² j in moving a particle from the origin along the x-axis to (1, 0), then along the line to (0, 1), and then back to the origin along the y-axis. segment cycloid and us 21. (a) If C is the the point ( S (b) If the verti are (x₁, y₁. the polygo A = 1/[(x₁ (c) Find the a (1, 3), (0, 22. Let D be a reg xy-plane. Use nates of the ce 1 2A where A is the x = 23. Use Exercise region of radi 24. Use Exercise vertices (0, 0) 25. A plane lamin region in the Show that its Ix = - 26. Use Exercise disk of radius (Compare wit 27. Use the metho F and C is any E encloses the c 28. Calculate fe F C is the SILI
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