2.
f x f x dx
n
f x n1 c
f x f x dx
n
n 1
3.
f x f x dx
n
f x n1 c
f x f x dx
n
n 1
d
e.g. i a) Find
dx
1 x
3
4.
f x f x dx
n
f x n1 c
f x f x dx
n
n 1
d
e.g. i a) Find
dx
d
dx
1 x
3
1
1
1 x 3 1 x 3 2 3 x 2
2
3x 2
2 1 x3
9. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2
10. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
11. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
12. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
13. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u 2 x2
14. b) Hence find;
x2
dx
3
1 x
x2
2 3x 2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u 2 x2
du
2x
dx
du 2 xdx
15. b) Hence find;
x2
dx
3
1 x
2 3x 2
x2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u
u 2 x2
du
2x
dx
du 2 xdx
16. b) Hence find;
x2
dx
3
1 x
2 3x 2
x2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
1
du
2
u
u 2 x2
du
2x
dx
du 2 xdx
17. b) Hence find;
x2
dx
3
1 x
2 3x 2
x2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u
1
du
2
1
1 2
u du
2
u 2 x2
du
2x
dx
du 2 xdx
18. b) Hence find;
x2
dx
3
1 x
2 3x 2
x2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u
1
du
2
1
1 2
u du
2
3
1 2 2
u c
2 3
u 2 x2
du
2x
dx
du 2 xdx
19. b) Hence find;
x2
dx
3
1 x
2 3x 2
x2
dx
dx
3
3
3 2 1 x
1 x
2
1 x3 c
3
ii x 2 x 2 dx
OR
1
2 x 2 x 2 dx
2
3
1 2
2 x 2 2 c
2 3
1
2 x 2 2 x 2 c
3
x 2 x 2 dx
u 2 x2
du
2x
dx
du 2 xdx
u
1
du
2
1
1 2
u du
2
3
1 2 2
u c
2 3
1
2 x 2 2 x 2 c
3