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.
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. 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.
(7) Green's Theorem for Work in the Plane F(x, y) =< M, N >=< x, y2 > C: CCW once about y = vw and y = x W = | <M,N><dx,dy>= | Mdx + Ndy CZ CZ (70) Parametrize the path Cy: along the curve y = vw from (1,1) to (0,0) in terms of t. (70) Use this parametrization to find the work done. (7e) Confirm Green's Theorem for Work. (7) Green's Theorem for Work in the Plane...
3. (12 points) Evaluate the line integral S y3dx + (x3 + 3xy2)dy , where C is the path from (0,0) to (1,1) along the graph y = x3 and from (1,1) to (0,0) along the graph of y=x.
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction 3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...
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)
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Let C be a triangle in the x-y plane with vertices (x1,y1), (x2y2) and (x3,y3) arranged so that C is positively-oriented. Let C be a triangle in the xy-plane with vertices (x,y), (z2,p), and (z3,U3) arranged so that C is positively-oriented. a.) Sketch such a triangle and indicate its orientation. b.) Apply Green's Theorem to compute the area of the triangle as a (sum of) path integral(s) around the boundary. Get a formula for area in terms of the coordinates...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...