Question 3 (6 points) a problem of practical concern which was considered by newton and a number of other pioneers of calculus was the volume of a wine barrel. in this question, we will instead consider the related question of how much work is needed to pump wine from a barrel. suppose we have a barrel, 4 feet tall, which is positioned with its base at y = −2 and its top at y = 2. suppose in addition that the radius of the circular slice of the barrel at height y is 2 − y 2 8 . how much work is needed to pump a full barrel of wine out a spout in the top of the barrel? (a) (3 points) set up an integral to compute the necessary work. you may use g to denote the acceleration due to gravity and d to denote the density of wine.