Question

(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along the helix 7(t) s(2cost, 2sint, t) (3) for 0 st s Tt/4 in two ways. (a) Using the parametric curve (t) and integrating forO π/4. By finding a potential function and integrating from (2,0,0) to (V2, 2,T/4) (b)

Answer 1

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