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11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the plane x= 0.

11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the plane x= 0.

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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a) Evaluate F-dr b) Show that F a conservative vector field Find a functionf such that Vf = F L.F dī again. d) Use the results of b) and c) to evaluate ·dr 6. Given F(x, y, z) =(8x' +z?, -3z,2xz -3 y), Easily add text in PDF Add 7. Evaluate xyddx +e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola y = 2x - x from (2,0) to (0,0). 8. Find the work done by F = (x - y,x) along C:7(t) = (2cos t, 2sint) 0sts 27 : a) Without Green's theorem b) With Green's theorem. 9. Evaluate F dĩ ;where F = (y'cos x, x²+2ysin x) and C is the triangle from (0,0) to (2,6) to (2,0) to (0,0). 10. Given F = (x*y, yz²,-2z²x*), find a) curl F b) div F ([ +z?)dS where S is the part of the paraboloid x=4 - y² - ? that lies in front of 11. Evaluate the plane x =0. 12. Evaluate the surface integral [[F ds for the vector field F(x, y, z) = (-x,-y,z), where S is the part of the cone z=lx + y? between the planes z=1 and z =3 with downward orientation. F-dī ; where F(x, y, z) = (1,x+ yz, xy - (): 13. Evaluate and C is the boundary part of the plane 3x+2 y+z=1 in the first octant. Answers 1. 96
Transcribed Image Text:a) Evaluate F-dr b) Show that F a conservative vector field Find a functionf such that Vf = F L.F dī again. d) Use the results of b) and c) to evaluate ·dr 6. Given F(x, y, z) =(8x' +z?, -3z,2xz -3 y), Easily add text in PDF Add 7. Evaluate xyddx +e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola y = 2x - x from (2,0) to (0,0). 8. Find the work done by F = (x - y,x) along C:7(t) = (2cos t, 2sint) 0sts 27 : a) Without Green's theorem b) With Green's theorem. 9. Evaluate F dĩ ;where F = (y'cos x, x²+2ysin x) and C is the triangle from (0,0) to (2,6) to (2,0) to (0,0). 10. Given F = (x*y, yz²,-2z²x*), find a) curl F b) div F ([ +z?)dS where S is the part of the paraboloid x=4 - y² - ? that lies in front of 11. Evaluate the plane x =0. 12. Evaluate the surface integral [[F ds for the vector field F(x, y, z) = (-x,-y,z), where S is the part of the cone z=lx + y? between the planes z=1 and z =3 with downward orientation. F-dī ; where F(x, y, z) = (1,x+ yz, xy - (): 13. Evaluate and C is the boundary part of the plane 3x+2 y+z=1 in the first octant. Answers 1. 96
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