Consider the function f given by f(x, y, z) = xz. Find the average value of the function f over the region F in the first octant bounded by the coordinate planes and the parabolic cylinders z = 9 - x and y = 9 - x. XCertainly! Let's go ahead and compute the integral to find the average value of the function at, 3;, z] = M over the region F in the first octant bounded by the coordinate planes and the parabolic cylinders z = 9 1:2 and y = 9 :2. Limits of Integration: " Form:0::a::3. " Fory:D:Zg<2. forz:gz the average value of f is given by: :ez dz dydm integrating :2 over region f: at n94 :22 dy fan do: i o with respect to z lirst. then y. and finally a: :1: w l ole: ina d3 evaluating integral: eden this integral can be simplified using a substitution. let so that do="25rda:." substituting. becomes:>