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.
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...
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.
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. ∮C 6 ln(6+y) dx−(xy/6+y) dy, where C is the triangle with vertices (0,0), (6,0), and (0,12) ∮C 6 ln(6+y) dx−(xy/6+y)dy=
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. ху 7 In(7 + y) dx - dy, where C is the triangle with vertices (0,0), (4,0), and (0,8) fe 7+ y ху f 7 ln(7 + y) dx – dy = 7+y
10. [8 points] Use Green's Theorem to evaluate the line integral Sexy dx + (x2 + y) dy, where the closed curve C determined by y=x2 and y - =2 between (-1,1) and (2, 4). Sketch the curve and the region enclosed by the curve.
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...
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.