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3. (12 points) Evaluate the line integral S y3dx + (x3 + 3xy2)dy , where C...
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line s...
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy,...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0)...
5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0) to (1, 1) along the graph of y = x3 and from (1, 1) to (0,0) along the graph of y = x oriented in the counterclockwise direction. a) Calculate the line integral using Green's Theorem. b) Calculate the same line integral using definition.
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1,...
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. T...
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. Theorerm to compute ф F-ds where Fay3 dx + (x343xy?) dy and C is the path that you drew in 11a.
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the...
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C...
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy
10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the...
10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the parabola y = x2 from (0,0) to (2,4).
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations...
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0)...
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. Theorerm to compute ф F-ds where Fay3 dx + (x343xy?) dy and C is the path that you drew in 11a.
Green's Theorem )dy - (4y2 ex)dx Evaluate Y Here, y is the path along the boundary...
Green's Theorem )dy - (4y2 ex)dx Evaluate Y Here, y is the path along the boundary of the square from (0,0) to (0,1) to (1,1) to (1,0) to (0,0) State Green's Theorem in its entirety. Sketch the curve, y. Indicate the given orientation on the curve. Explain in detail how all the conditions of the hypothesis of the theorem are satisfied. Use Green's Theorem to evaluate the given integral. Simplify your answer completely.
Green's Theorem )dy - (4y2 ex)dx Evaluate...
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0) to (1, 1) along the graph of y = x3 and from (1, 1) to (0,0) along the graph of y = x oriented in the counterclockwise direction. a) Calculate the line integral using Green's Theorem. b) Calculate the same line integral using definition.
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. Theorerm to compute ф F-ds where Fay3 dx + (x343xy?) dy and C is the path that you drew in 11a.
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the...
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy
10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the parabola y = x2 from (0,0) to (2,4).
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. Theorerm to compute ф F-ds where Fay3 dx + (x343xy?) dy and C is the path that you drew in 11a.
Green's Theorem )dy - (4y2 ex)dx Evaluate Y Here, y is the path along the boundary of the square from (0,0) to (0,1) to (1,1) to (1,0) to (0,0) State Green's Theorem in its entirety. Sketch the curve, y. Indicate the given orientation on the curve. Explain in detail how all the conditions of the hypothesis of the theorem are satisfied. Use Green's Theorem to evaluate the given integral. Simplify your answer completely.
Green's Theorem )dy - (4y2 ex)dx Evaluate...
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