EXERCISE SET 7.8 Graphing Utility CCAS 1. In each part, determine whether the integral is improper, and if so, explain why. /2 sin.x /4 sec² x 23. dx 24. dx tan x 1/3 √1-2 cos x (a) L dx dx dx dx (b) (c) In.x dx x-3 x+3 25. 26. ox-2 -2x (d) J dx dx ex dx (e) tan.x dx 27. X dx 28. 70 Jo (x-1)2/3 2. In each part, determine all values of p for which the integral +00 1 dx is improper. 29. dx 30. 70 x√√x²-1 dx dx (a) (b) (c) e -px dx XP 31. x-p 11. dx dx 32. √x(x+1) √x(x+1) 3-32 Evaluate the integrals that converge. +oo. 3. e -2x dx x 4. dx 33. 2 5. dx 6. xe dx 7. dx 8. dx x In³x xvInx dx 9. 10. (2x-1)³ L dx x²+9 11. 1. Le e3x dx 12. ex dx 3-2ex 00 13. xdx 14. x dx 33-36 True-False Determine whether the statement is true or false. Explain your answer. -4/3 x dx converges to 3. 34. If f is continuous on [a, +) and lim,+f(x) = 1, then f(x) dx converges. 35. ـم 1 x(x-3) dx is an improper integral. 36. dx = 0 x 15. dx 16. (x²+3)2 √x²+2 1+e-2 dr 37-40 Make the u-substitution and evaluate the resulting defi- nite integral. 37. 17. 6 dx dx 38. 18. o (x-4)2 √x 39. dx 19. tan x dx 20. 0 √√4-x dx xdx +00 -x 21. 22. 40. S S +00 [Note: u 1 as x+oo.] dx; u = ex dx; u = dx √x [Note: u+oo as x→+oo.] ;u= √√x [Note: u+oo as x+o0.] √√x(x+4)* e-x dx; u=1-ex -x² √√9-x2 0 √√1-e-2x