Let `f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot` Then the value of `|"cos"(f(pi))|` is____

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| is___

Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) is __________

Let f(x)=sin[pi/6sin(pi/2sinx)] for all x in RR

If f(x)=|x|^(|sinx|), then find f^(prime)(-pi/4)

If int_(sinx)^(1)t^(2)f(t)dt=1-sinx, xepsilon(0,(pi)/2) then find the value of f(1/(sqrt(3)))

if f(x)= sinx + cosx for 0 < x < pi/2

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^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

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dxdot

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The value of int_(0)^(pi//2) f(x)dx is