MATH 2400 Quiz: Quiz7Solutions
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July 25, 2012: if s is the sphere of radius 16 centered at the origin, parameterize the portion of s contained in the rst octant. In spherical coordinates, the sphere is given by the equation = 16. ~r(u, v) = h16 cos sin , 16 sin sin , 16 cos i . Since we are only want the portion in the rst octant, we have the bounds. 2: calculate the line integral of the vector eld ~f = (cid:10)y2, xy(cid:11) along the curve y = x3 from (0, 0) to (1, 1). ~f d~r = z 1: let c be any smooth curve starting at (1, 3) and ending at (0, 1). 0 (cid:10)(x3)2, x(x3)(cid:11) (cid:10)dx, 3x2dx(cid:11) = z 1 the line integral of ~f (x, y) = (cid:10)2x + 5y, 5x 3y2(cid:11) along c. Note that ~f is a conservative vector eld.
