This is a limit of Riemann sums! Specifically, it is a limit of Riemann sums of {{MATH_120}} rectangles, where {{MATH_121}} {{MATH_122}} {{MATH_123}} and {{MATH_124}} Hence, we may rewrite this as {{MATH_125}} {{CMD_126}} The limit computes the area between the {{MATH_127}}-axis and the curve {{MATH_128}}. Let's see it: {{CMD_129}} {{ENV_130}} {{CMD_131}} By geometry, we know that this semicircle has area {{MATH_132}}. Hence {{MATH_133}} {{CMD_134}} {{CMD_135}} {{CMD_136}} {{CMD_137}}