Section 15.1: Double Integrals over rectangles

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 \(2 \le x \le 4\), \(2 \le y \le 6\). 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.