I need help on these!

Signature: Show your work completely to get full credit. My signature above indicates that I have completed this exam without any help from outside resources 1. (8 points) Evaluate the integral using the Tabular method. x cos 2xdx 2. (8 points) Write the partial fraction decomposition of the rational expression. Do not determine the numerical values of the coefficients. -3x + 51 (x2 -16)(4x? - 20x +25)(x3 +4) (8 points) Evaluate sec 3x tan3xv9-tan-3x -dx using the formula provided from an Integral Table du a+ Na -u uva6. (8 points) Find the area of the region bounded by the graphs of two functions y = x -4x and y = 2x . 7. (8 points) CHOOSE ONE ONLY! I. A cable that weighs 3 1b/ft is used to lift 500 lb of coal up a mine shaft 300 ft II. deep. Find the work done. (8 points) A force of 2 N will stretch a rubber band 2 em. Assuming that Hooke's Law applies, (a) How far will a 4N force stretch the rubber band? b) How much work does it take to stretch the rubber band this far ( We need the answer in part (a) to do it)?\f4. (20 points) Find the volume generated by rotating the region bounded by the curve y = x and the line x = 1 and the x-axis. Just set up the integrals. Do not evaluate them, and name the method that you are using. a. about the x-axis. About the y-axis. c. about the line x = 1 about the line y (40 points) Evaluate each integral (a) [ese xet * dx