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 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: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

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

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(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

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 f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

Let f(x) be a continuous function such that int_(n)^(n+1) f(x) dx=n^(3) , ninZ . Then the value of the integeral int_(-3)^(3) f(x) dx, is

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

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