MAT 266 Test 1 1 Directions: 1. There are 14 questions worth a total of 60 points. 2. Questions 1 - 10 are Multiple Choice/ True/False worth 4 points each to be answered on the supplied SCANTRONS 3. Questions 11 - 14 are Free Responses worth 5 points each and are to be answered in the space provided on the test. 4. Read all the questions carefully. 5. For the Free Response, you must show all work in order to receive credit!! When possible, box your answer, which must be complete, organized, and exact unless otherwise directed. 6. Always indicate how a calculator was used (i.e. sketch graph, etc. …). 7. No calculators with QWERTY keyboards or ones like TI-89 or TI-92 that do symbolic algebra may be used. Honor Statement: By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor. _______________________________________ _________________ Signature Date MAT 266 SPRING 2012 TEST 1 SoMSS, ASUMAT 266 Test 1 2 1. Evaluate the integral: 223ydyy  Select the correct answer. a. 12tan ( 3)yC b. 22ln | 3|yC c. 2ln( 3)yC d. 22ln | 3|y y C e. none of these 2. Evaluate the integral using integration by parts with the indicated choices of u and dv: 4 lnx x dx Select the correct answer. a. 222 lnx x x C b. 222 lnx x x C c. 22 lnx x x C d. 222 ln 4x x x C e. none of these 3. Use the given formula to evaluate the integral: 22141dyyy (Formula: 2222 2 2du u aCauu u a) Select the correct answer. a. 241y y C b. 2[ 4 1/ ]y y C c. 241yC d. 2[ 4 1/ ]y y C e. none of theseMAT 266 Test 1 3 4. Select the correct answer for ( )cos( ( )) f x f x dx from the options given below: a. sin( ( ))f x C b. sin( ( ))f x C c. sin | ( )|f x C d. sin()xCfx e. None of these. 5. The form of the partial fractions expansion of the rational function32225( 1) ( 3)xxxx is: a. 22( 1) ( 3)ABxx b. 22( 1) 1 ( 3)A B Cx x x c. 22( 1) 1 3 ( 3)A B C Dx x x x      d. 22( 1) 1 ( 3)A B Cx Dx x x e. None of these 6. For the integral 2216dxxx choose the appropriate trig-substitution from the list provided below: Select the correct answer. a) 4sinx b) 4tanx c) 4secx d) 4cosx e) None of the above 7. Using the trig-substitution from Problem # 6 above, the resulting trigonometric integral in its simplified form is: a) 1tan 4d b) 1sin 4d c) 1cos 16d d) 1sec 16d e) None of theseMAT 266 Test 1 4 8. Use the Trapezoidal Rule to approximate dxex32/3 for n = 4. Select the correct answer. The choices are rounded to four decimal places. a. 3.4215 b. 3.4437 c. 3.4227 d. 3.5227 e. None of these. 9. Evaluate the integral: 22tan secx x dx Select the correct answer. a. tan | |xC b. 2sec tanx x C c. secxC d. 2tan xC e. none of these 10. Select the appropriate substitution from the list given below that would simplify the evaluation of the integral 3arctan211yedyy a. 21uy b. arctanuy c. tanuy d. 21/(1 )uy e. None of theseMAT 266 Test 1 5 FREE RESPONSE 11. [5 pts] Evaluate the integral: 4 tte dt 12. [5 pts] Evaluate the integral: 52cos sin x x dxMAT 266 Test 1 6 13. [5 pts] Find the exact value of /420cos x dx 14. [5 pts] Evaluate the integral: dxxxx