The number of critical points of the function`f(x) =int_0^x e^t(t-1)(t-2)(t-3)dt`

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the points of minima for f(x)=int_(0)^(x)t(t-1)(t-2)dt

The set of critical points of the function f(x) given by f(x)= x - log _(e)x + int((1)/(t)-2-2cos 4t) dt is

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

The interval in which the function f(x)=int_(0)^(x) ((t)/(t+2)-1/t)dt will be non- increasing is