sin4xcos6xdx f(x)=sin4xcos6x Since, sinx is an odd function and sin2x is an even function and cos6x is an even function. So, f(x) is an even function. ∴
2π
∫
−2π
sin4xcos6xdx=2
2π
∫
0
sin4xcos6xdx [∵∫−aaf(x)dx=2
a
∫
0
f(x)dx] =2×2
π
∫
0
sin4xcos6xdx [∵
nπ
∫
0
f(x)dx=n
T
∫
0
f(x)dx] =4
π
∫
0
sin4xcos6xdx =4×2
π
2
∫
0
sin4xcos6xdx [∵
2a
∫
0
f(x)dx=2
a
∫
0
f(x)dx] =8
π
2
∫
0
sin4xcos6xdx [∵ If m and n are both even, then
