Let `"Let"(x)=|{:(,2sinx,sin^(2)x,0),(,1,2sin x,sin^(2)x),(,0,1,2sin x):}|`, then find determinent

Let f(x)= |{:(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0):}| ,"then find " 1/piint_0^(pi/2)[f(x)+f'(x)]dx.

Let F (x) = [{:(cos x , -sin x , 0),(sin x , cos x , 0),(0 , 0, 1):}] , then

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 ^(2) x,,sin 2x,,-sin x),(sin 2x,,2 sin^(2)x,,cos x),(sin x,,-cos x,,0):}| .then 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)| , then 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)| , then 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)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

If f(x)=|(sin x+sin 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1)|, then the value of int_0^(pi/2) f(x) dx is

Evaluation of definite integrals by subsitiution and properties of its : f(x)=|(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1)| then int_(0)^(pi/2)f(x)dx=……….

If 1+sin x sin ^(2)""(x)/(2) = 0 then x is