MATH 151 TEST 2 11 20 07 FALL 2007 Remember to keep your work neat and orderly Show all of your work NO WORK NO CREDIT Read each question carefully and be sure to answer the question that was asked Calculator answers are not acceptable Name pts 1 Integrate each of the following 0 a 3e 2x dx c 2x 1 x 5 2 4dx 2 Integrate some more 3 b x ln x dx 2 d 3 0 2 dx x 1 5 7 8 7 a 3x sin 4 x dx 3 Find the partial fractions expansion of 2x 3 dx b 2 x 5x 4 x2 7x 6 x x 2 x 3 4 Use the tables in the back of the book to integrate 7 6 evaluate the constants 7 9 4x2 dx x2 Give the number of the formula you used 7 5 Find another set of polar coordinates with 0 2 that corresponds to the given point in polar coordinates a 11 5 6 b 7 0 5 3 3 6 Sketch the graph use your calculator and then set up do not evaluate an integral that will r 5 cos 3 give the total area enclosed by the graph of the polar curve 9 x t 6 y t 4 7 For the parametric equation eliminate the parameter and sketch the graph Show and label the coordinates of the starting point and the direction of motion 7 y sin 2t x e 3t 0 t 1 8 Given the parametric curve a Find the slope of the tangent line to the graph at t 0 6 b Set up do not evaluate an integral in parametric form with a dt that will give the area under the curve and above the x axis 5 c Set up do not evaluate an integral in parametric form with a dt that will give the volume of the solid if the curve is revolved around the x axis 6 12 9 Evaluate completely 2 6 cos d 0 7