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Question 2 Consider these problems. Consider the region (shown above) bounded by the graphs of y = (x -2)2 and y = 4. When this region is revolved about the x axis, what is the volume of the resulting solid? When this region is revolved about the horizontal line y = 4, what is the volume of the resulting solid? Plan the approach for each problem. Advice: set up (but do not evaluate) integrals to solve these problems on paper. Then, answer the following questions: method of disks When the region is revolved about the x-axis, we can use the method of washers . When the region is revolved about the horizontal line y = 4, we can use the method of washers method of disks The "radius" or "radii" will be different for each problem. A student considered several possible integrals: A ) T So ( 4 - ( 20 - 2 ) 2 ) dac B) ISa [(x - 2)2]2 + 42) dx C) TT So (42 - [(z -2)2]") da . Integral finds the volume of the solid when the region is revolved about the x-axis. I MU IMU . Integral finds the volume of the solid when the region is revolved about the line y = 4.Question 3 Consider this problem. Water is drained from a swimming pool at a rate given by r (t) = 100e F gallons per hour, where k = 20. If the pool could drain forever (infinite time), how much water would drain from the pool? Step through the solution. Advice: solve the problem on paper. Then, answer the following questions. The total amount of water drained is given by the integral of the rate function over the infinite time interval: So 100e E dt improper This integral is undefined divergent indeterminate A student worked out the antiderivative of 100e . They considered several possibilities: A) 100e B) - 100k . e F C) 100 - F The correct antiderivative is possibility After the student applied the evaluation theorem, and after they completed some algebra steps, they needed to take this limit: lim - 20 b -+ 0o They considered several possibilities: A) O B) 1 C) OC The correct limit is possibility