Find the flux of the vector field F = ( - y,x, 1) across the cylinder y = 3x", for 0 Sx$ 3, 0 szs 4. Normal vectors point in the general direction of the positive y-axis. Parametrizationsing u = x and v = z. Set up the integral that gives the flux as a double integral over a region R in the uv-plane. JJ Funds= SSD du av S R (Type exact answers.)Find the area of the following surface using a parametric description of the surface. The plane 2= 17 - x- 3y above the square |x| 52, M 52 E} Set up the integral for the surface area using the parameterization u = x and v = y. DD II(D) dudv 2 2 (Type an exact answers, using 1c as needed.) Evaluate the surface integral II f(x,y,z) dS using a parametric description of the surface. S f(x,y,z) = 3x, where S is the cylinder x2 + z2 = 36, for 0 S y 51 Write a parametric description of the given cylinder using u = 6 and v = y. r(u,v) = (ELDD where 0 S u S D and D SV 5 El (Type exact answers.) Find the area of the following surface using the given explicit description of the surface. The paraboloid z = 3 (x2 + yz) , for 0 s z s 27 (I) Set up the surface integral for the given function over the given surface S as a double integral over a region R in the xyplane. Uww (Type an exact answer, using I: as needed.) Evaluate the surface integral f(x,y,z) dS using an explicit representation of the surface. f(x,y,z) = 5xy; S is the plane z = 2 - x - y in the first octant. Set up the surface integral for the given function f(x,y,z) over the given surface S. Integrate with respect to x first. Use increasing limits of integration. 00 f(x,y,z) as = ] ] () dx dy S (Type exact answers.)