Logarithmic functions - integration - basic.
Test Yourself 1.
Integrate each of the following indefinite integrals:
1. | 2. |
3. | 4. |
5. Find the primitive of . | 6. Find the primitive of . |
7. . | 8. Integrate . |
9. Integrate |
10. |
11. |
12. |
13. | 14. |
15. | 16. . |
17. (i) Show that
(ii) Hence find . |
18. |
19. | 20. |
Evaluate each of the following definite integrals:
21. .
Answer.e2 - 1 + ln 3. |
22.
Answer.2 - ln 3. |
23. | 24. |
25. can be written in the form
(i) Find the values of A and B. Hint.Begin by creating a 4x using the denominator - so multiply by 2.Then consider what you need in the second term to recreate the original expression in the numerator. (ii) Hence find . Answer.(i) a = 2 and b = -5.(ii) 4 - 5ln 5. |
26. (i) if the velocity (v) of a particle is described by the equation , (where t is the time during which the particle has been moving), what is the value of v when t = 0?
Answer.(i) 1 m/sec (ii) 6.23 m. |
27. (i) Sketch the graph of .
(ii) Show that . (iii) Hence use the Trapezoidal Rule with three function values to find an approximation to ln 3 (to 4 significant figures). (iv) Repeat the above step using 5 function values. (v) Explain the differences between your two values and the exact value of ln 3. Answer.(ii) 1.367.(iii) 1.117. (iv) ln 3 = 1.099. |
28. |