If `f(x)=int(sinx)/(cos^(2)x)(1-3sin^(3)x)dx`, then value of `(f(0)-f(pi)+(9pi)/2)` is

Let F(x)=int_(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)] , then

If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) ((sqrt(pi))/(2)) and (gof)((pi)/(3)) .

If f(x)=sin^(-1)(3x-4x^(3)). Then answer the following The value of f'((1)/(sqrt2)) , 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) = |{:(cos x ,e^(x^(2)),2xcos^(2)((x)/(2))),(x^(2),secx,sinx+x),(1,2,x+tanx):}| the value of f_(-pi//2)^(pi//2)(x^(2)+1) [f(x)+f''(x)]dx is

If f'(x)=sinx+sin4x.cosx, then f'(2x^(2)+pi/2) is

If number of solution and sum of solution of the equation 3sin^(2)x-7sinx +2=0, x in [0,2pi] are respectively N and S and f_(n)(theta)=sin^(n)theta +cos^(n) theta . On the basis of above information , answer the following questions. If alpha is solution of equation 3sin^(2)x-7sinx+2=0, x in [0,2pi] , then the value of f_(4)(alpha) is

The function f(x)= (sin 3x)^(tan^(2)3x) is continuous at x= (pi)/(6) then f((pi)/(6)) = ……

If (cos3x)/(cosx)=1/3 for some angle x,0<=x<=pi/2 then the value of (sin3x)/(sinx) for some x is