Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = (2x3 + y3)i + (y3 + z3)j + 3y2zk, s is the surface of the solid bounded by the paraboloid z = 1 − x2 − y2 and the xy-plane.

has divergence

Then by the divergence theorem, the flux of across is equal to the integral of over the interior of . In cylindrical coordinates, this integral is

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1