Question

Let ∫ sin9 𝑥 cos(11𝑥) 𝑑𝑥 = cos(10𝑥) 𝑓(𝑥) + 𝑐 , where 𝑐 is a constant. If 𝑓 ′′ ($\frac{\pi}{4}$) − 𝑘𝑓 ′($\frac{ \pi}{4}$) = 0, then 𝑘 is equal to ______ (in integer)

Answer 1

The correct answer is: 8