We now consider some examples
Example 27 Evaluate the following integrals:
(i)
3
2
∫2 x dx
(ii)
9
3
4
22
(30–
)
x
dx
x
∫
(iii)
2
1 (
1) (
2)
x dx
x
x
+
+
∫
(iv)   
3
4
0 sin 2 cos 2
t
t dt
π
∫
Solution
(i)
Let 
3
2
2
I
= ∫x dx Since 
3
2
F ( )
x3
x dx
x
=
=
∫
,
Therefore, by the second fundamental theorem, we get
I = 
27
8
19
F (3) – F (2)
–
3
3
3
=
=
(ii)
Let 
9
3
4
2
2
I
(30 –
)
x
dx
x
= ∫ We first find the anti derivative of the integrand Put 
23
3
30 –