(7) Green's Theorem for Work in the Plane F(x, y) =< M, N >=< x, y2...
(7) Green's Theorem for Work in the Plane F(x, y) =< M, N >=< xy, x + y > C: CCW once around y = x² + y2 = 1 W = <M,N><dx,dy> = | Mdx + Ndy C (7a) Parametrize the path C in terms of t. (76) Use this parametrization to find the work done.
(6) Fundamental Theorem of Line Integrals F = <M,N> = < 2xy, x² + y2 > (6a) Show that F is a Conservative Vector Field. (6b) Find the Potential Function f(x,y) for the Vector Field F. (60) Evaluate W = | Mdx + Ndy from (5,0) to (0,4) over the path C: È + K3 = 1 с
Use Green's Theorem to evaluate the line integral. (x - 97) dx + (x + y) dy C: boundary of the region lying between the graphs of x2 + y2 = 1 and x2 + y2 = 81 x-9
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...
Given two functions, M(x, y) and N(x,y), suppose that ON/ that an/az-amay is M-N a function of x +y. That is, let f(t) be a function such that ON _ OM dc du f(x+y) = M-N Assume that you can solve the differential equation Mdx + Ndy = 0 by multiplying by an integrating factor u that makes it exact and that it can also be written as a function of x + y, u = g(x + y) for...
Can you evaluate without Green's Theorem?
If so, please show your work.
Suppose that f(x, y) has continuous second-order partial derivatives, and let C be the unit circle oriented counterclockwise. What is / [fx(x, y) – 2y] dx + [fy(x, y) + x] dy?
Use Green's Theorem to calculate the line integral f. 2xy dx + 2(x+y) dy, where C is the unit circle centered at the origin and it is counter-clockwise oriented. $c 2xy dx + 2(x + y) dy =
WITH ALL STEPS SHOWN
ay+y?)dx- xdywhere C is the closed curve 3. Verify Green's Theorem in the plane for of the region bounded by y = x and y = x2.
ay+y?)dx- xdywhere C is the closed curve 3. Verify Green's Theorem in the plane for of the region bounded by y = x and y = x2.
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...
Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y
Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y