Logarithmic functions - integration - basic.
Test Yourself 1.
Integrate each of the following indefinite integrals:
1. | 2. |
3. | 4. |
5. The primitive is |
6. The primitive is . |
7. | 8. Integrate |
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11. |
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15. | 16. |
17. (i)
(ii) |
18. |
19. | 20. |
Evaluate each of the following definite integrals:
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25. (i) Find the values of A and B. (ii) |
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27.
(i) (ii) (iii)
(iv)
(v) The more function values used, the closer the successive trapeziums align with the curve. Using 3 function values overestimates the area between the curve and the x axis by about 6.1% (1.167 compared to ln 3 (=1.099)). Using 5 function values still overestimates reduces this overestimate from 1.167 to 1.117 which is much less - only 1.16%. |
28. |