If `f(x)` is a function satisfying `f(x+a)+f(x)=0` for all `x in R` and positive constant `a` such that `int_b^(c+b)f(x)dx` is independent of `b ,` then find the least positive value of `cdot`

If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all nonzero x, then evaluate int_(sin theta)f(x)dx

Let f:Rvec R be a function given by f(x)=ax+b for all x in R. Find the constants a and b such that fof=I_(R)

If f(x+1)+f(x+7)=0,x in R, then possible value of t for which int_(a)^(a+t)f(x)dx is independent of a is

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b Least positive value fo c if c,k,b are n A.P. is

If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) 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 fandg are continuous function on [0,a] satisfying f(x)=f(a-x)andg(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx