A function f is defined by `f(x)=int_(0)^(pi)cost cos(x-t)dt, 0 le x le2pi`. Then which of the following hold(s) good ?

A function f is defined by f(x) = int_0^pi cos t cos(x-t)dt,0 <= x <= 2 pi then which of the following.hold(s) good?

A function f is defined by f(x)=int_0^pi costcos(x-t)dt, 0lexle2pi . Which of the following hold(s) good? (A) f(x) is continuous but not differentiable in (0,2pi) (B) There exists at least one c in (0,2pi) such that f\'(c)=0 (C) Maximum value of f is pi/2 (D) Minimum value of f is -pi/2

A differentiable function satisfies f(x) = int_(0)^(x) (f(t) cot t - cos(t - x))dt . Which of the following hold(s) good?

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Let (dy)/(dx) + y = f(x) where y is a continuous function of x with y(0) = 1 and f(x) = {{:(e^(-x), if o le x le 2),(e^(-2),if x gt 2):} Which of the following hold(s) good ?

If f(x) =int_(0)^(x) sin^(4)t dt , then f(x+2pi) is equal to

For x epsilon(0,(5pi)/2) , definite f(x)=int_(0)^(x)sqrt(t) sin t dt . Then f has

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi , Then, f(x) is

Find the intervals in which f(x)=log(cosx), 0 le x le 2pi is increasing.