Let f be a non-negative function defined on `[0,1]`. if
`int_(0)^(x)sqrt(1-(f^(')(t))^(2))dt`=`int_(0)^(x)f(t)dt,0<=x<=1`,and`f(0)`=0 then

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ f(0)=0 , then

Let f be a function defined on the interval [0,2pi] such that int_(0)^(x)(f^(')(t)-sin2t)dt=int_(x)^(0)f(t)tantdt and f(0)=1 . Then the maximum value of f(x) is…………………..

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

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

Let f be a differentiable function on R and satisfying the integral equation x int_(0)^(x)f(t)dt-int_(0)^(x)tf(x-t)dt=e^(x)-1 AA x in R . Then f(1) equals to ___

Let f(x) be a differentiable non-decreasing function such that int_(0)^(x)(f(t))^(3)dt=(1)/(x^(2))(int_(0)^(x)f(x)dt)^(3)AAx inR-{0} andf(1)="1. If "int_(0)^(x)f(t)dt=g(x)" then "(xg'(x))/(g(x)) is

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of int_(0)^(pi//2) f(x)dx lies in the interval

If int_(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals