Andrew Baird Saoub MAT 266 Spring 2009 12245 WeBWorK assignment number Section 6.2 is due : 02/04/2009 at 11:59pm MST. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA?s or your professor for help. Don?t spend a lot of time guessing ? it?s not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2^3 instead of 8, sin(3 pi=2)instead of -1, e^(ln(2)) instead of 2, (2+tan(3)) (4 sin(5))^6 7=8 instead of 27620.3413, etc. Here?s the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 1. (1 pt) Evaluate the indefinite integral.Z sin3(8x)cos2(8x)dx +C Correct Answers: -cos(8 * x)**(3)/(3 *8)+ cos(8 * x)**(5)/(5 * 8) 2. (1 pt) Evaluate the indefinite integral.Z 15cos3(86x)dx Answer = +C Correct Answers: 15/86*sin(86*x) - 15/(3*86)*(sin(86*x))**3 3. (1 pt) Z p=4 0 sin4(4x)dx = Correct Answers: 0.2945243113125 4. (1 pt) Evaluate the indefinite integral.Z 56cos2(53x)dx Answer = +C Correct Answers: 56*x/2 + 56*sin(2*53*x)/(4*53) 5. (1 pt) Evaluate the indefinite integral.Z xsin2(9x)dx Answer = +C Correct Answers: (9*x?2 - x*sin(2*9*x) - cos(2*9*x)/(2*9))/(4*9) 6. (1 pt) Evaluate the definite integral.Z 10 2 sin2(5x)cos2(5x)dx Correct Answers: 1.01011506536058 7. (1 pt) Evaluate the indefinite integral. Z 1+2sinx cosx dx +C Correct Answers: 1*ln(abs(sec(x)+tan(x)))+2*ln(abs(sec(x))) 8. (1 pt) Evaluate the integral.Z sec2 x tan1 x dx +C Correct Answers: tan(x)**(1+1)/(1+1) 9. (1 pt) Evaluate the integral. Z 2p=4 0 sec4(t=2)dt Correct Answers: 2.66666666666667 10. (1 pt) Evaluate the indefinite integral.Z tan2(4x)dx Answer = +C Correct Answers: tan(4*x)/4 - x 11. (1 pt) Evaluate the indefinite integral.Z tan4(4x)dx Answer = +C Correct Answers: tan(4*x)**3/(3*4) - tan(4*x)/4+x 12. (1 pt) Evaluate the indefinite integral.Z tan3(4x)sec5(4x)dx Answer = +C Correct Answers: sec(4*x)**7/(7*4) - sec(4*x)?5/(5*4) 13. (1 pt) Evaluate the indefinite integral. Z 4 4tan2 x 8sec2 x dx Answer = +C Correct Answers: 4*sin(2*x)/(2*-8) 1 14. (1 pt) Evaluate the indefinite integral.Z sin(3x)cos(7x) dx Hint: Use the identity sinAcosB= 12[sin(A B)+sin(A+B)] Answer = +C Correct Answers: -0.5 * (cos((3+ 7)*x)/(3 + 7) + cos((3 - 7)*x)/(3 - 7)) 15. (1 pt) For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS. A. x = 6tanq B. x = 6sinq C. x = 6secq 1. Z x2 p 36+x2 dx 2. Z p x2 36dx 3. Z dx (36+x2)3 4. Z (x2 36)5=2 dx 5. Z x2 dx p36 x2 Correct Answers: A C A C B 16. (1 pt) Evaluate the definite integral.Z 7sin(p3 ) 0 x3p 49 x2 dx Correct Answers: 71.4583333333333 17. (1 pt) Evaluate the definite integral.Z 6 0 x3 p x2 +36 dx Correct Answers: 2503.05662146842 18. (1 pt) Evaluate the indefinite integral.Z 85 x2p64x2 400dx Correct Answers: 85*((64*(x**2)-400)**.5)/(400*x) Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 2