If `f(a+b-x) =f(x)` , then `int_(a)^(b) x f(x) dx ` is equal to

int_(a+c)^(b+c) f(x) dx is equal to

If f(x)=f(a+b-x), then int_(a)^(b) xf(x)dx is equal to

If f(a+x)=f(x), then int_(0)^(na) f(x)dx is equal to (n in N)

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

If f(x) =(x-1)/(x+1),f^(2)(x)=f(f(x)),……..,……..f^(k+1)(x)=f(f^(k)(x)) ,k=1,2,3,……and g(x)=f^(1998)(x) then int_(1//e)^(1) g(x)dx is equal to

If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

If a lt b lt c in R and f (a + b +c - x) = f (x) for all, x then int_(a)^(b) (x(f(x) + f(x + c))dx)/(a + b) is:

If f((3x-4)/(3x+4))=x+2 , then int f(x)dx is equal to

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to