Home
Class 12
MATHS
Find a function g:R rarr R, continous in...

Find a function `g:R rarr R,` continous in `[0,infty)` and positive in `(0,infty)` satisfying `g (0)=1` and `(1)/(2)int_(0)^(x) g^(2)(t)dt=(1)/(x)(int_(0)^(x) g (t) dt)^(2)`

Promotional Banner

Similar Questions

Explore conceptually related problems

Find a function g:RrarrR , continuous in [0,oo) and positive in (0,oo) satisfying g(1)=1 and 1/2int_0^xg^2(t)dt=1/x(int_0^xg(t)dt)^2

If g(x) is continuous function in [0, oo) satisfying g(1) = 1. If int_(0)^(x) 2x . g^(2)(t)dt = (int_(0)^(x) 2g(x - t)dt)^(2) , find g(x).

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

lim_(xrarroo)((int_(0)^(x)e^(t^(2))dt)^(2))/(int_(0)^(x)e^(2t^(2))dt) is equal to

If int_(0)^(x) f(t)dt=x^(2)+2x-int_(0)^(x) tf(t)dt, x in (0,oo) . Then, f(x) is

lim_(x to 0)(int_(0)^(x^(2))(tan^(-1)t)dt)/(int_(0)^(x^(2))sin sqrt(t)dt) is equal to :

lim_(x to 0)(int_(0^(x) x e^(t^(2))dt)/(1+x-e^(x)) is equal to

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

lim_(x rarr 0) (int_(0)^(x) t tan(5t)dt)/(x^(3)) is equal to :