e , f is an odd function Therefore, by P7 (ii), I = 0
INTEGRALS         345
Example 34 Evaluate 
4
2
4
4
0
sinsin
cos
x
dx
x
x
π
+
∫
Solution Let I = 
4
2
4
4
0
sinsin
cos
x
dx
x
x
π
+
∫ (1)
Then, by P4
I =
4
2
0
4
4
sin (
)
2
sin (
)
cos (
)
2
2
x
dx
x
x
π
π −
π
π
−
+
−
∫
 = 
4
2
4
4
0
coscos
sin
x
dx
x
x
π
+
∫