Find the average value of f(x,y) = sin (x + y) over a. the rectangle OSxSn/S, OSyS111c/6 b. the rectangle 05x52n/3, OSySu/Z E) a. The average value of f is |:. (Type an exact answer, using at as needed.) 30,000 ey If f(x,y) = W represents the "population density" of a certain bacterium on the 1 + 4 xyplane, where x and y are measured in centimeters, nd the total population of bacteria within the rectangle - 4 5x5 4 and -1 S y S 0. Express the total population of bacteria as an iterated integral. 4 o 30,0005Y j _W -4 -1 \" 4 Evaluate the integral in the previous step. The exact value of the integral is