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Problem 2. (6 pts total) An eating contest has broken out, and Atalanta wants to win. Atalanta needs to eat a block of cheese that is shaped like a rectangular prism, with width and height 3 centimeters, and length L centimeters. She will start eating the block from the left end of its length. The caloric density of the cheese is p(x) kCal/cm3 at the point a cm from the left end. As Atalanta eats, the crowd notices her progress and cheers her on; encouraged, her ability to quickly ingest calories increases. Therefore, there is a function A(x) modeling her eating speed (in kCal/s) when she has eaten the leftmost a cm of the block. The goal of this problem is to explain how to write a definite integral formula, using the given functions and constants, representing how long it takes Atalanta to eat this block of cheese. You may provide sketches as part of your explanation. (a) (1 pt) Explain a plan to break this problem up into parts, providing the notation you will use. (b) (2 pts) Explain how you are approximationg a piece of the solution on one of your individual parts. Be specific in explaining what you are approximationg, and any choices you are making to approx- imate it. Units are an important part of this explanation. (c) (1 pt) Use the result of part (b) to come up with an expression for the approximate time it takes Atalanta to eat the whole block of cheese. (d) (2 pts) Use your answer to part (c) to explain how to obtain a definite integral formula for the exact time it takes Atalanta to eat the whole block of cheese; use appropriate mathematical notation to relate your answer from part (c) to this definite integral formula