Sketch the region of integration. Write an equivalent iterated integral with the order of integration reversed. Choose one of the two orders of integration and evaluate the iterated integral you chose by hand. Explain the reasoning behind your choice. Determine the exact average value of cos ( y 3 ) over the region D that is determined by the iterated integral I .

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.