dA R is the region bounded by the graphs xy- 1, xy 4, x 1, x 4 R 1+x2y2 15.1 Vector Fields 19. Consider F(x, y,z) . Find a. curl(F) b. div(F) 15.2 Line Integrals 20. J xy ds where c(t)0sts1 21. h x2 + y2 + z2 ds where c(t) 0 t 22. Evaluate J x +4Vy ds over a. C: traverse the x-axis from (0,0) to (1,0), then along the line y-x 1 from 1,0) to (2,1) C: counterclockwise around the square with vertices (0,0), (2,0), (0,2), (2,2) b. 23. Evaluate the work done by F(x,y) along the curve c(t) - cos(t) 1+ sin(t) 24. Evaluate f (2x-y)da (x + 3y)dy over the arc C: y 1-x2 from (0,1) to (1,0) 15.3 Conservative fields 25. Determine if the following are conservative b. F(x,y) 2xyi (x2 - y)j c. F(x,y) 2xyi (x - y2)j d. F(x,y,z) 2xy(x2z2))2yz k
Show transcribed image text dA R is the region bounded by the graphs xy- 1, xy 4, x 1, x 4 R 1+x2y2 15.1 Vector Fields 19. Consider F(x, y,z) . Find a. curl(F) b. div(F) 15.2 Line Integrals 20. J xy ds where c(t)0sts1 21. h x2 + y2 + z2 ds where c(t) 0 t 22. Evaluate J x +4Vy ds over a. C: traverse the x-axis from (0,0) to (1,0), then along the line y-x 1 from 1,0) to (2,1) C: counterclockwise around the square with vertices (0,0), (2,0), (0,2), (2,2) b. 23. Evaluate the work done by F(x,y) along the curve c(t) - cos(t) 1+ sin(t) 24. Evaluate f (2x-y)da (x + 3y)dy over the arc C: y 1-x2 from (0,1) to (1,0) 15.3 Conservative fields 25. Determine if the following are conservative b. F(x,y) 2xyi (x2 - y)j c. F(x,y) 2xyi (x - y2)j d. F(x,y,z) 2xy(x2z2))2yz k