Chapter 15.1, Problem 5E

Let V be the volume of the solid that lies under the graph of $f(x,y)=\sqrt{52-x^2-y^2}$ and above the rectangle given by 2 ≤ x ≤ 4, 2 ≤ y ≤ 6. Use the lines x = 3 and y = 4 to divide R into subrectangles. Let L and U be the Riemann sums computed using lower left corners and upper right corners, respectively. Without calculating the numbers V, L, and U, arrange them in increasing order and explain your reasoning.