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line integral lestvins 3 12. Evaluate line integral for the vector field E=(²,-xy) along the curve A(-2,-3) to B(2,1). Answer: 32.8 13 6 13. If F=xyi-y² j, evaluate fF-dr where C is the curve y=2x² in the xy-plane from (0,0) to (1,2). Answer: 14. Evaluate clockwise in the xy-plane x=0, x=4 and y = 0, y = 2. Answer: -32 1/2²+x F-dr where E=(x² + y²)i-2xyj and C is the rectangle with counter- +x-3 from 79 5 15. Find the work done in moving a particle in a force field given by F=(xy,-5z,2x) along the curve x = t² +1, y = 2t²,z=t³ where 1st≤2. Answer: 16. Evaluate F-nds where F=(182,-12,3y) and S is the surface of the plane 2x+3y+6z=12 in the first octant. Answer: 24 2 17. Suppose vector field F=(z,x,3y), find the flux integral of the surface S, x+3z=3 bounded by plane y=0, y=3 x=0 and z=0 as shown in Figure 1.

line integral lestvins 3 12. Evaluate line integral for the vector field E=(²,-xy) along the curve A(-2,-3) to B(2,1). Answer: 32.8 13 6 13. If F=xyi-y² j, evaluate fF-dr where C is the curve y=2x² in the xy-plane from (0,0) to (1,2). Answer: 14. Evaluate clockwise in the xy-plane x=0, x=4 and y = 0, y = 2. Answer: -32 1/2²+x F-dr where E=(x² + y²)i-2xyj and C is the rectangle with counter- +x-3 from 79 5 15. Find the work done in moving a particle in a force field given by F=(xy,-5z,2x) along the curve x = t² +1, y = 2t²,z=t³ where 1st≤2. Answer: 16. Evaluate F-nds where F=(182,-12,3y) and S is the surface of the plane 2x+3y+6z=12 in the first octant. Answer: 24 2 17. Suppose vector field F=(z,x,3y), find the flux integral of the surface S, x+3z=3 bounded by plane y=0, y=3 x=0 and z=0 as shown in Figure 1.

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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12. Evaluate line integral for the vector field F=(y-xy) along the curve y 2 A(-2,-3) to B(2,1). Answer: 32.8 13. If F=xyi-y² j, evaluate to (1,2). Answer: 13 6 Answer: 14. Evaluate F-dr where clockwise in the xy-plane x=0, x=4 and y = 0, y = 2. Answer: -32 15. Find the work done in moving a particle in a force field given by F=(xy,-5z,2x) along the curve x = t² +1, y = 2t²,z=t³ where 1st≤2. 79 5 F-dr where C is the curve y=2x² in the xy-plane from (0,0) Page 108 12+x-3 from E=(x² + y²)i-2xyj and C is the rectangle with counter- Answer: 42 16. Evaluate F-nds where F=(182,-12,3y) and S is the surface of the plane 2x+3y+6z=12 in the first octant. Answer: 24 17. Suppose vector field F=(z,x,3y), find the flux integral of the surface S, x+3z=3 bounded by plane y=0, y=3 x=0 and z=0 as shown in Figure 1. Figure 1.
Transcribed Image Text:12. Evaluate line integral for the vector field F=(y-xy) along the curve y 2 A(-2,-3) to B(2,1). Answer: 32.8 13. If F=xyi-y² j, evaluate to (1,2). Answer: 13 6 Answer: 14. Evaluate F-dr where clockwise in the xy-plane x=0, x=4 and y = 0, y = 2. Answer: -32 15. Find the work done in moving a particle in a force field given by F=(xy,-5z,2x) along the curve x = t² +1, y = 2t²,z=t³ where 1st≤2. 79 5 F-dr where C is the curve y=2x² in the xy-plane from (0,0) Page 108 12+x-3 from E=(x² + y²)i-2xyj and C is the rectangle with counter- Answer: 42 16. Evaluate F-nds where F=(182,-12,3y) and S is the surface of the plane 2x+3y+6z=12 in the first octant. Answer: 24 17. Suppose vector field F=(z,x,3y), find the flux integral of the surface S, x+3z=3 bounded by plane y=0, y=3 x=0 and z=0 as shown in Figure 1. Figure 1.
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