1. Consider the solid of revolution revolving the region bounded by y = {5. y = 2, and :r = U about the :r-axis. [a] In the graph provided below, sketch a graph of the region (ED) of revolution and indicate the axis of rotation using a rotating arrow. Shade in the region of revolution. The entire region should be visible in the graph. Number the axes so that all important points ean be read. [b] Use the diskg'washer method to express the volume of the solid as an integral. {c} Find the volume of the solid by evaluating the integral found in part [b]. 2. onsider the solid of revolution revolving the region hounded by a = 3;; ~ ya and :1: = 1; about the :r:-a:-ris. {a} In the graph provided below, sketch a graph of the region {21]} of revolution and indicate the axis of rotation using a rotating arrow. Shade in the region of revolution. The entire region should be visible in the graph. Number the axes so that all important points can he read. [11) Use the shell method to express the volume of the solid as an integral. (c) Find the volume of the solid by evaluating the integral found in part {b}. 3. Consider the solid of revolution revolting the region bounded by .r = 2;; and y = 3 with s 2 0 about the y-axis. This solid consists of water with a 1straight. of Su lbs f ft\". [a] In the graph provided belowI sketch a graph of the region {2D} of revolution and indicate the axis of rotation using a rotating arrow. Shade in the region of revolution. The entire region should be visible in the graph. Number the axes so that all important points can be read. ' " [b] Express the work needed to pump the liquid to the top of the container at y = 3 as an integral. {o} Find the work needed to pump the liquid by evaluating the integral found in part {b}. 4. Evaluate the following integrals. Be sure to include all work for the computation. (a) (x4 - 5x2) In(z) dr (b) (12 - 3x) cos NIH dx5. Use trigonometric substitution to evaluate the integral below. dx 4-12 Do not use any other method for this. Other methods will not receive any credit. Show all the steps involved in the computation. Express your final answer in algebraic terms as much as possible.6. Consider the rational function f(z) = 3 + 5x - 12 x(12+ 4) (a) State the form of the partial fraction decomposition of the rational function above. Use undetermined coefficients (i.e. letters such as A, B, C, etc.) to denote unknown numbers. (b) Find the undetermined coefficients in the partial fraction decomposition stated in part (a). Show all steps in the computation. (c) Use your answer from part (b) to evaluate the integral 3x2 +5x -12 dr I(x2 +4) Show all steps involved in the computation