See the attached file for questioins

2.         The graphs of the functions f(x) = x³ and g(x) = x meet at two places. Revolve the region enclosed by these two graphs around the y-axis. What is the volume of the volume of revolution?

            The enclosed area in the first quadrant is:

3.         Use an integral to calculate the volume of a sphere of radius 4 with a cylindrical hole of radius 2 drilled through its center.

4.         A cup of soy milk weighs 243 grams = 0.243 kg and contains 131 nutritional calories. If one drinks the cup in three sips, each time lifting the cup 40 cm = 0.4 m and drinking a third of it, how much work is expended on the act of drinking? Considering the work expended on drinking, what is the net caloric intake resulting from drinking this cup? Neglect the weight of the cup itself. (Hint: It is important to keep track of the units of work (Newtons Newton-meters, or Joules) and convert them to energy units of nutritional calories. To calculate Newtons, the mass must be in kg and the distance in meters.

5.         Find the anti-derivative of:

6.         Use the definition of improper integral to evaluate the given integral: