Directions: Show ALL work under each item below. Your work shown should justify your answers and convince me of your thinking. No work shown may result in a loss of points. Box your final answers. 1. Imagine that you have a butternut squash that is 8 inches tall (not counting the stem), like the one pictured below, and you wish to determine the volume of this vegetable. With the curved shaped, you will need to use calculus (integration) to figure that out! Go to the following Desmos page to answer the following questions: https://www.desmos.com/calculator/pfr9vizn51 a. Find a function that best models the shape of the butternut squash in the first quadrant (you can ignore the stem). In effect, this function will model the curvy side shape of the squash. You can use Desmos to figure this out! Write your function in the space below. [10 pts] b. Imagine rotating the function you created above around the horizontal axis to create a solid. With this in mind, create an integral that will calculate the volume of the butternut squash. Write the integral in the space below, then integrate to find the volume (include units in your final answer). Show all your integration steps! [15 pts]