Question

I only need 4,5,6please show all your work, perferably on a seprate sheet of paper.Thank you.

Find the average value of f(x, y,z) = xyz over x2 + y2 + z2 2, z > 0, x > 0. y>0. Evaluate the surface integral (x,y,1) dS, where S is the portion of the paraboloid z = 1 - x2 - y2 that lies over the unit disk. Evaluate the line integral of F(x,y,z) = (x,-y2,z), where c(r) - (sin t, cos t.2t) from t = 0 to t = pi. Express as an equivalent integral in the order dydzdx: Use the transformation u - x + y, v - x - y to find where D is the region enclosed by the lines x+y=0, x+y=l, x-y= 1, x-y=4. Find the surface integral of V x where t(x,y,z) - (z - y, z + x, - x - y) over the portion of the paraboloid z - 9- x2 -y2 above the xy-plane.