x - Balliol College - University of Oxford
x - Balliol College - University of Oxford
x - Balliol College - University of Oxford
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SJ Roberts - July 2011 Revision 1/ page 4<br />
2 Integration<br />
You should understand the difference between a definite and an<br />
indefinite integral. You should be able to integrate simple functions by<br />
recognising them as differentials <strong>of</strong> familiar functions:<br />
b<br />
11. <br />
a<br />
3 x 2 dx<br />
12. x<br />
4 x<br />
3 dx<br />
5<br />
x<br />
13. sin x cos x dx<br />
14. dx<br />
1 x<br />
2<br />
be able to manipulate functions so that more complex functions become<br />
recognisable for integration:<br />
2<br />
15. sin<br />
0<br />
2<br />
x dx<br />
16. tan x dx<br />
change variables, e.g. using<br />
to integrate functions such as:<br />
x sin<br />
or other trigonometric expressions<br />
1<br />
17. dx<br />
1 x<br />
2<br />
<br />
18*. dx<br />
a x<br />
2<br />
2<br />
1<br />
use integration by parts for certain more complex functions:<br />
19. x sin x dx
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