If `f(x)=e^x+int_0^(sinx)(e^t dt)/(cos^2x+2tsinx-t^2) AA x in (-pi/2,pi/2),then`

f(x)=int_(0)^(x)(e^(t)-1)(t-1)(sin t-cos t)sin tdt,AA x in(-(pi)/(2),2 pi) then f(x) is decreasing in :

f(x)=int_0^x(e^t-1)(t-1)(sint-cost)sin t dt ,AAx in (-pi/2, 2pi), then f(x) is decreasing in :

If f(x)= int_(0^(sinx) cos^(-1)t dt +int_(0)^(cosx) sin^(-1)t dt, 0 lt x lt (pi)/(2) then f(pi//4) is equal to

If f(x)= int_(0^(sinx) cos^(-1)t dt +int_(0)^(cosx) sin^(-1)t dt, 0 lt x lt (pi)/(2) then f(pi//4) is equal to

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) pi/(2sqrt(2))

Find the differentiable function which satisfies the equation f(x)=-int_(0)^(x)f(t)tan tdt+int_(0)^(x)tan(t-x)dt where x in(-(pi)/(2),(pi)/(2))

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

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

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

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