Let `f(x)=|2cos^2xsin2x-sinxsin2x2sin^2xcosxsinx-cosx0|` . Then the value of `int_0^(pi//2)[f(x)+f^(prime)(x)]dx` is a.`pi` b. `pi//2` c.`2pi` d. `3pi//2`

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)|, the value of int_0^(pi//2){f(x) + f'(x)} dx, is

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)|, the value of int_0^(pi//2){f(x) + f'(x)} dx, is (i)pi/2 (ii)pi (iii)(3pi)/2 (iv)2pi

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(x)=int(sin2x(cos2x-cos4x))/(cos2x(cos2x+cos4x))dx then the value of f((pi)/(3))-f(0) is

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

If f(x)=cos ec(x-(pi)/(3))cos ec(x-(pi)/(6)) then the value of int_(0)^((pi)/(2))f(x)dx is

Let f(x)=sin x+2cos^(2)x,x in[(pi)/(6),(2 pi)/(3)] then maximum value of f(x) is

int_(0)^(pi//2)sin x.sin 2x dx=