`f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,cos^2x,cos^2x)|` then `int_0^(pi/2) f(x) dx=.....`

Let f(x) = |{:(secx,cosx,sec^(2)x+cotx cosecx),(cos^(2)x,cos^(2)x,cosec^(2)x),(1,cos^(2)x,cos^(2)x):}| then find the value of f_(0)^(pi//2) f(x) dx.

Let f(x)=|sec x cos x sec^(2)x+cot x cos ecx cos^(2)x cos^(2)x cos ec^(2)x1cos^(2)x cos^(2)x Prove that int_(0)^((pi)/(2))f(x)dx=-(pi)/(4)-(8)/(15)

int_0^(pi//2) x^2 cos 2x dx

int_0^pi (cos^2x)dx ,

Let f(x)=det[[sec^(2)x,1,1cos^(2)x,cos^(2)x,cos ec^(2)x1,cos^(2)x,cot^(2)x]], then

f(x)=cot^(2)x*cos^(2)x, g(x)=cot^(2)x-cos^(2)x

int(sec x+2cot^(2)x+cos^(2)x)/(cos x)dx

If f(x) = |(x,cos x,e^(x^(2))),(sin x,x^(2),sec x),(tan x,1,2)| , then the value of int_(-pi//2)^(pi//2) f(x) dx is equal to

f(x)=cos x*cos2x*cos4x*cos8x.cos16x then find f'((pi)/(4))