If p,q,r and s are in AP and f(x) =`|{:(p+sinx,q+sinx,p-r+sinx),(q+sinx,r+sinx,-1+sinx),(r+sinx,s+sinx,s-q+sinx):}|` such that `f_(0)^(1)`f(x) dx =-2, the common difference of the AP can be

If p,q,r and s are in AP and f(x) = |{:(p+sinx,q+sinx,q-r+sinx),(q+sinx,r+sinx,-1+sinx),(r+sinx,s+sinx,s-q+sinx):}| such that int_(0)^(1) f(x) dx =-2, the common difference of the AP can be

If p,q,r,s are in A.P.and f(x)=|(p+sinx,q+sinx,p-r+sinx),(q+sinx,r+sinx,-1+sinx),(r+sinx,s+sinx,s-q+sinx)| such that int_0^2 f(x) dx=-4 then the common difference of the A.P. can be : (A) 1 (B) 3/2 (C) -1 (D) 3

If f(x)= =|{:(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1):}| then the value of int_(0)^(pi//2) f(x)dx , is

If f(x)=|{:(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1):}|," then the value of "int_(0)^(pi//2)f(x)dx is

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

If f(x)=|(cosx,cosx,sinx),(-cosx,cosx,-sinx),(sinx,sinx,cosx)| , then find its determinant

The domain fo f(x)=(1)/(|sinx|+sinx) is

If f(x) = |{:(sinx,cosx,sinx),(cosx,-sinx,cosx),(x,1,1):}| find the value of 2(f'(o))+{f'(1)}^(2)

If f(x) =|{:(sinx,cosx,sinx),(cosx,-sinx,cosx),(x,1,1):}| find the value of 2[f'(0)]+[f'(1)]^(2)