Let `f(x),xgeq0,` be a non-negative continuous function. If `f^(prime)(x)cosxlt=f(x)sinxAAxgeq0,` then find `f((5pi)/3)`

Let f(x),x>=0, be a non-negative continuous function,and let F(x)=int_(0)^(x)f(t)dt,x>=0, if for some c>0,f(x) =0, then show that f(x)=0 for all x>=0.

Let f(x) be a non-negative continuous function defined on R such that f(x)+ f(x+(1)/(2))=3 ,then the value of (1)/(1008)*int_(0)^(2016)f(x)dx

Let f(x) be a non-negative continuous function defined on R such that f(x)+f(x+1/2)=3 , then the value of 1/1008 int_(0) ^(2015) f(x) dx is

Let f(x) be the continuous function such that f(x)= (1-e^(x))/(x) for x!=0 then

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

Discuss the continuity of the function f given f(x)=|x| at x=0

Let f(x) be a continuous function such that f(0)=1 and f(x)=f((x)/(7))=(x)/(7)AA x in R then f(42) is

If a continuous function f on [0,a] satis fies f(x)f(a-x)=1,a>0 then find the value of int_(0)^(a)(dx)/(1+f(x))

Let [x] denote the integral part of x in R and g(x)=x-[x]. Let f(x) be any continuous function with f(0)=f(1) then the function h(x)=f(g(x)