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 x f(x) dx = a/2 int_0 ^a f(x) dx`

Property 5: If f(x) is a continuous function defined on [0;a] then int_(0)^(a)f(x)dx=int_(0)f(a-x)dx

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

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

Property 6: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

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 continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

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

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even