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Problem: C is the positively oriented curve starting at the point (0, 0), moving along y = 0 to the point 30 (5,0), then along the circle x² + y² = 25 to the point (0,5), and then along x = 0 back to (0, 0). Use Green's Theorem to evaluate f (x²y dx - xy² dy). Integrals

Problem: C is the positively oriented curve starting at the point (0, 0), moving along y = 0 to the point 30 (5,0), then along the circle x² + y² = 25 to the point (0,5), and then along x = 0 back to (0, 0). Use Green's Theorem to evaluate f (x²y dx - xy² dy). Integrals

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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Only problem 30
Problem: C is the rectangle with vertices (0,0), (4,0), (4,3), and (0,3). F is the vector field F = (xy, x²). Use Green's Theorem to determine § F T ds. Use Green's Theorem to determine 25 F.N ds. 26 C. F is the vector field F = (y², 3xy). Use Green's Theorem to determine § F.T ds. Then use , and the line segment from (1, 0) to (2, 0). R is the region enclosed by Green's Theorem to determine § FN ds. Problem: Consider the vector field F = (4y - tan x sec x)i + (8x + In y²) j. Suppose C is the circle x² + y² = 64. Use Green's Theorem to evaluate F. dR. Problem: Use Green's Theorem to determine the area of the region that is enclosed by the curves x = y² 27 and x = y + 2. Problem: Use Green's Theorem to determine the area of the region that is enclosed by the curves xy = 6 28 and x + y = 7. 29 Problem: C is the triangle formed by the lines connecting (0,0) to (4,0) to (4,12) to (0,0). Use Green's Theorem to evaluate the line integral (xy dx + x²y dy). 31 Problem: C is the positively oriented curve starting at the point (0, 0), moving along y = 0 to the point 30 (5,0), then along the circle x² + y² = 25 to the point (0,5), and then along x = 0 back to (0, 0). Use Green's Theorem to evaluate f (x²y dx - xy² dy). Integrals Problem: C is the circle x² + y² = 9 and R is the region inside the circle. Use Green's Theorem to evaluate f (x dx + x² dy). y- to evaluate the integral bian needed to the ind Problem: Green's Theorem provides an easy way to calculate the area inside any polygon if the vertices 32 are known. Use this procedure as discussed in class to calculate the area of the pentagon if the vertices are (-4,8), (1, 12), (7,6), (3,0),(-1,2).
Transcribed Image Text:Problem: C is the rectangle with vertices (0,0), (4,0), (4,3), and (0,3). F is the vector field F = (xy, x²). Use Green's Theorem to determine § F T ds. Use Green's Theorem to determine 25 F.N ds. 26 C. F is the vector field F = (y², 3xy). Use Green's Theorem to determine § F.T ds. Then use , and the line segment from (1, 0) to (2, 0). R is the region enclosed by Green's Theorem to determine § FN ds. Problem: Consider the vector field F = (4y - tan x sec x)i + (8x + In y²) j. Suppose C is the circle x² + y² = 64. Use Green's Theorem to evaluate F. dR. Problem: Use Green's Theorem to determine the area of the region that is enclosed by the curves x = y² 27 and x = y + 2. Problem: Use Green's Theorem to determine the area of the region that is enclosed by the curves xy = 6 28 and x + y = 7. 29 Problem: C is the triangle formed by the lines connecting (0,0) to (4,0) to (4,12) to (0,0). Use Green's Theorem to evaluate the line integral (xy dx + x²y dy). 31 Problem: C is the positively oriented curve starting at the point (0, 0), moving along y = 0 to the point 30 (5,0), then along the circle x² + y² = 25 to the point (0,5), and then along x = 0 back to (0, 0). Use Green's Theorem to evaluate f (x²y dx - xy² dy). Integrals Problem: C is the circle x² + y² = 9 and R is the region inside the circle. Use Green's Theorem to evaluate f (x dx + x² dy). y- to evaluate the integral bian needed to the ind Problem: Green's Theorem provides an easy way to calculate the area inside any polygon if the vertices 32 are known. Use this procedure as discussed in class to calculate the area of the pentagon if the vertices are (-4,8), (1, 12), (7,6), (3,0),(-1,2).
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