Let f : R `to` R be a continuous function satisfying
`f(x)+underset(0)overset(x)(f)"tf"(t)"dt"+x^(2)=0`
for all `"x"inR`. Then-

Let f: R rarr R be a continous function satisfying f(x) = x + int_(0)^(x) f(t) dt , for all x in R . Then the numbr of elements in the set S = {x in R: f (x) = 0} is -

Let f:R rarr R be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt. Then the value of f(1n5) is

Let f : R rarr R be a continuous function which satisfies f(x) = int_0^x f(t) dt . Then the value of f(log_e 5) is

Let f:RtoR be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt . Then the value of f(log_(e)5) is

Let S be the set of real numbers p such that there is no nonzero continuous function f: R to R satisfying int_(0)^(x) f(t) dt= p f(x) for all x in R . Then S is

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=underset(0)overset(x)intf(t)dt , then

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to