(Solved): parts a and c please Activity 6.2.4. In each of the following questions, draw a careful, labeled sk ...

Activity 6.2.4. In each of the following questions, draw a careful, labeled sketch of the region described, as well as the resulting solid that results from revolving the region about the stated axis. In addition, draw a representative slice and state the volume of that slice, along with a definite integral whose value is the volume of the entire solid. It is not necessary to evaluate the integrals you find. For each prompt, use the finite region $$S$$ in the first quadrant bounded by the curves $$y=2x$$ and $$y=x^3$$. a. Revolve $$S$$ about the line $$y=?2$$. b. Revolve $$S$$ about the line $$y=4$$. c. Revolve $$S$$ about the line $$x=?1$$. d. Revolve $$S$$ about the line $$x=5$$.