ENGR 251 Midterm: ENGR 251 Midterm 2005 Fall
Document Summary
Do not assume we can read your mind! Compute the curl and the divergence of the vector. ~f (x, y, z) = yzexi + (2x 3yz)j + xy2z3k. Evaluate the following integral by reversing the order of integration: ~f (x, y) = (2xy)i + (x2)j: show that this vector eld is conservative, i. e. the line integrals rc independent of path, and nd a function (x, y) such that ~f = . ~f d~r are: let c be the upper half of the circle x2 + y2 = 1 in the xy plane, going from the point (1, 0) to ( 1, 0). Compute the work done by the force ~f along the curve. C in two di erent ways: (i) using the function found in part (a). (ii) computing the line integral rc tween the endpoints. ~f d~r directly along any convenient path be- By using the appropriate theorem (which must be named) compute the circulation hc.
