If f(x)= sin⁡x+sin⁡2x+sin⁡3xsin⁡2xsin⁡3x3+4sin⁡x34sin⁡x1+sin⁡xsin⁡x1 then the value of ∫0π/2 f(x)dx is

By applying the operation C1→C1−C2−C3,f(x) can be written as f(x)=sin⁡xsin⁡2xsin⁡3x034sin⁡x0sin⁡x1=sin⁡x3−4sin2⁡x=sin⁡3xSo ∫0π/2 f(x)dx=−cos⁡3x30π/2=13.