ii) Evaluate the following line integral: gdl. Where g = 20xy for line element from: a)...
Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t) Problem 1. (16.2 Line Integrals) Evaluate the line integral Jc xeids, where C is the line segment from (0,0,0) to (1.2,3).(t,at,3t)
6. Evaluate the line integral Skyds where of yox from (0,0) to (ii).... is the ar
please help with parts b and c! I do not understand how to find F. Thank you! 7. Find the line integral of F-(6x2-6x) i +6z j + k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. b.C2: r(t)-ti+12 j+14 k, 0sts1 c. C3UC4: the path consisting of the line segment from (0,0,0) to (1.1,0) followed by the segment from (1,1,0) to (1,1,1) a. The line integral of F over C1 is b. The...
Find the line integral of F = (3x^2-7x) i +7z j + k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. a. C1: r(t) = t i + t j + t k, b: C2: r(t) = t i +t^2 j + t^4 k, c: C3C4: the path consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) We were unable to transcribe this imageWe were unable...
3. [4 marks] Evaluate the following line integral by two methods: (i) directly and (ii) by using the Green's Theorem ferds – ydy where is the circle r' + y2 = 9. S. 3
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 +...
10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the parabola y = x2 from (0,0) to (2,4).
Evaluate the line integral, where C is the given curve. where C is the curve of intersection of the sphere and the plane oriented counterclockwise when viewed from the positive x-axis. We were unable to transcribe this image-- + +22=1 r - y=0
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from (3,0) to (0,4) in the xy-plane.
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2) 3. Let (a) Show that F is conservative...