V. Integration Of Exponential Functions
Integrate with respect to x the following functions:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25.
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
*37. 
38. Evaluate the following integrations
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
(g) 
(h) 
[ans: (a) e (b) 
(c) 
(d) 9/2 (e) 3/8 (f) 3/ln2 (g) 0.009/ln10
(h) 
]
39. Show that 
. Use this result to evaluate 
[ans: 1]
40. Show that 
, hence evaluate 
[ans: 1/2]
41. Find the area enclosed between:
(a) the curve 
, the ordinates x = 0 and x = 1 and the x-axis. [ans: e-1]
(b) the curve 
, the ordinates x = 0 and x = 2 and the x-axis.
[ans: 
]
(c) the curve 
, the ordinates x = 0 and x = 1 and the x-axis. [ans: 
]
*(d) the curve 
, the ordinates x = 1 and x = 2 and the x-axis.
[ans: 
]
(e) the curve 
, the ordinates x = 0 and x = 1 and the x-axis. [ans: 
]