If af(x)+b`f((1)/(x))=(1)/(x)-5,x ne 0,a ne b`, then `overset(2)underset(1)int f(x)dx` equals

Let f(x+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?

If for nonzero x ,af(x)+bf(1/x)=1/x-5, where a!=b then int_1^2f(x)dx=

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

Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1)/(t))(1)/(t)dt , then

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

If f(x)dx=g(x) and f^(-1)(x) is differentiable, then intf^(-1)(x)dx equal to

If the roots of the equation (1)/(x+p)+(1)/(x+q)=(1)/(r ),(x ne -p, x ne -q, r ne 0) are equal in magnitude but opposite in sign, then p+q is equal to

If int f' (x) e^(x^(2)) dx = (x-1)e^(x^(2)) + c , then f (x) is

If f(x) is continuous for all real values of x , then sum_(r=1)^nint_0^1f(r-1+x)dx is equal to (a) int_0^nf(x)dx (b) int_0^1f(x)dx (c) int_0^1f(x)dx (d) (n-1)int_0^1f(x)dx