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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

9.

 

11.

 
13.  
15.

16.

17. (i)

(ii)

18.
19. 20.

Evaluate each of the following definite integrals:
21. 22.
23. 24.

25. (i) Find the values of A and B.

(ii)

26.
27.

(i)

(ii)

(iii)

x 0 1 2
1 1/2 1/3

(iv)

x 0 0.5 1 1.5 2
1 2/3 0.5 2/5 1/3

(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.