Task One: A basic model for the amount of energy required to lift an object a certain distance is given by E = WI . h. Here, W is the gravitational force calculated by the object's weight, and h is the height to which the object must be lifted. A 20m high structure (as depicted in the following GeoGebra applet) is to be constructed from the ground up (i.e. built piece-by-piece laying one small slab upon another). The structure is entirely solid, meaning that there are no gaps or hollow regions inside of the structure. The black arcs serve as the corner boundaries of the structure, and are formed from circles of radius 20. Specifically, the exterior walls of the structure run straight horizontally between the arcs at any given height. The arcs cross at the top of the structure, and run perpendicular to each other. Selecting the "Reveal Cross Section" removes two of the exterior walls so that the horizontal cross-section can be viewed at any particular height. Notice that at any height, the cross-section is a square, and D gives the distance from the center of the area to one of the arcs. h = 10 D = 17.32 Reveal Cross Section The structure is made of variable material for a varying mass with density function p() =many kilograms per cubic meters for a total mass of 240,000 kilograms. This function p should be interpreted as giving the density (i.e. mass per unit volume) of the structure's cross section at a height /. Importantly, this density is not uniform throughout the structure, and varies with height. Task: Calculate the total lifting energy required to build this structure from the ground up. You should first use a Riemann sum to estimate the total energy to within J Joules, and then write and evaluate a definite integral that will calculate the desired energy. Be sure to label each piece of the definite integral to show the weight-distance product being constructed, and to specify what each symbol in the integral formula means. Hint: You need to incorporate multiple basic models into this summation process to account for the weight of each small slab