The least value of `phi(x)= int_x^2 log_(1/3)t dt` for `x in (1/10 , 4)` is at `x=`

The least value of the function F(x) = int_(x)^(2) log_(1//3) t dt, x in [1//10,4] is at x=

The least value of expression 2 log_(10)x - log_(x) (1//100) for x gt 1 is:

The difference between the greatest and least values of the function F(x) = int_(0)^(x) (t+1) dt on [1,3] is

The difference between the greatest and the least values of the function f(x)=int_(0)^(x)(at^(2)+1+cos t)dt,a>0 for x in[2,3] is

The least value of the function phi(x)=int_(5pi//4)^(x) (3sin t+4 cos t)dt on the integral [5pi//4,4pi//3] , is

The difference between the greatest and least values of the function phi(x)=int_(0)^(x) (t+1) dt on [2,3], is\

The derivative of f(x)=int_(x^(2))^(x^(3))(1)/(log_(e)(t))dt,(x>0), is

If f(x) = int_1^x (1)/(2 + t^4) dt ,then

The value of lim_(x->0) cosec^4 x int_0^(x^2) (ln(1 +4t))/(t^2+1) dt is

If phi(x) = int_(1//x)^(sqrtx) sin(t^2) dt, then phi'(1) is equal to