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),x>=0, be a non-negative continuous function.If f'(x)cos x =0, then find f((5 pi)/(3))

Property 7: Let f(x) be a continuous function of x defined on [0;a] such that f(a-x)=f(x) then int_(0)^(a)xf(x)dx=(a)/(2)int_(0)^(a)f(x)dx

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

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

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)) .

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

Let f(x) be a continous function on R. If int_(0)^(1)[f(x)-f(2x)]dx=5 and int_(0)^(2)[f(x)-f(4x)]dx=10 then the value of int_(0)^(1)[f(x)-f(8x)]dx=

If for non zero x , 3f(x)+4f((1)/(x))=(1)/(x)-10 , then the value of int_(2)^(3)f(x)dx 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))