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. ‌∴
2Ï€
∫
−2π
sin‌4xcos6x‌dx=2‌
2Ï€
∫
0
sin‌4xcos6x‌dx ‌[∵∫−aaf(x)‌dx=2‌
a
∫
0
f(x)‌dx] ‌‌‌=2×2‌
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∫
0
sin‌4xcos6x‌dx ‌[∵
nπ
∫
0
f(x)‌dx=n‌
T
∫
0
f(x)‌dx] ‌‌‌=4‌
Ï€
∫
0
sin‌4xcos6x‌dx ‌‌‌=4×2‌
‌
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2
∫
0
sin‌4xcos6x‌dx ‌[∵
2a
∫
0
f(x)‌dx=2‌
a
∫
0
f(x)‌dx] ‌=8‌
‌
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2
∫
0
sin‌4xcos6x‌dx ‌[∵‌ If ‌m‌ and ‌n‌ are both even, then ‌ ‌
‌
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2
∫
0
sin‌mxcosnx‌dx= ‌‌
[(m−1)(m−3)...2‌ or ‌1][(n−1)(n−3)...2‌ or ‌1]