Unformatted text preview: F(r,y) = <*2y5, o*by"> on the plane is conscrvativc. (b) (6points) Findafunction / suchthar V.f =F, where F isthevecorfieldyou found in part (a). (c) (6 points) Find (by any method) J, f (r y). dr, where F is the vector field asked forin (a), and C isthepath -r= sin f, Jl= 1 + sin?t, -tt/ZK t < n/2. 4. (20 points) (a) (12 point^s) Express the integral t=rli=u, $/yz)sin(nx./y)dydx as an integral in new variables u and u, related to .r and y by the equations r = rr, ! = u/u. (You may take for granted that the above equations give a mapping that is one-to-one on its domain.) (b) (8 points) Evaluate the integral of (a) by any method. 5. (16 points) Find the maximum and minimum values of the function *2 * ,y * y2 on the circle *2 * yZ = 1, and list all points of the circle at which these values occur....
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This note was uploaded on 10/31/2009 for the course STAT 131A taught by Professor Isber during the Spring '08 term at Berkeley.
- Spring '08