Home
Class 12
MATHS
Let f(x) is a continuous function which ...

Let `f(x)` is a continuous function which takes positive values for `xgeq0` and satisfy `int_0^x f(t) dt= xsqrt(f(x))` with f(1)= 1/2 . Find the value of `f(sqrt2+1)`.

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) is a continuous function which takes positive values for x>=0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2. Find the value of f(sqrt(2)+1)

Let f(x) be a continuous function which takes positive values for xge0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2 . Then

If int_(0)^(x) f(t)dt=x+int_(x)^(1) t f(t) dt , then the value of f(1), is

If int_(0) ^(x) f (t) dt = x + int _(x ) ^(1) t f (t) dt, then the value of f (1) , is

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

f(x)=int_(0)^( pi)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is (1)/(2)

If f(x) is a continuous function such that f(x) gt 0 for all x gt 0 and (f(x))^(2020)=1+int_(0)^(x) f(t) dt , then the value of {f(2020)}^(2019) is equal to

Let f(x) be a continuous function defined for 0lexle3 , if f(x) takes irrational values for all x and f(1)=sqrt(2) , then evaluate f(1.5).f(2.5) .

Let f(x) be a continuous function defined from [0,2]rarr R and satisfying the equation int_(0)^(2)f(x)(x-f(x))dx=(2)/(3) then the value of 2f(1)