The set of critical pionts of the fuction f(x) given by
`f(x)= x - log _(e)x+underset(2)overset(x)((1)/(t)-2-2cos 4t)dt is `

If y = underset(u(x))overset(v(x))intf(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) If F(x) = underset(1)overset(x)inte^(t^(2)//2)(1-t^(2))dt , then d/(dx) F(x) at x = 1 is

Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)/(t))(1)/(t)dt , then

The poins of extremum of phi(x)=underset(1)overset(x)inte^(-t^(2)//2) (1-t^(2))dt are

If a function y=f(x) such that f'(x) is continuous function and satisfies (f(x))^(2)=k+underset(0)overset(x)int [{f(t)}^(2)+{f'(t)}^(2)]dt,k in R^(+) , then find f(x)

The number of critical points of f (x)= (int _(0) ^(x) (cos ^(2) t- ""^(3) sqrtt)dt)+3/4 x ^(4//3)-(x+1)/(2) in (0, 6pi] is:

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=underset(0)overset(x)intf(t)dt , then

The points of extremum of underset(0)overset(x^(2))int (t^(2)-5t+4)/(2+e^(t))dt are

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to

In (-4,4) the function f(x)=int_(-10)^x (t^2-4)e^(-4t) dt , has

If f(x)=overset(x)underset(0)int(sint)/(t)dt,xgt0, then