A Function `f(x)` satisfies the relation `f(x)=e^x+int_0^1e^xf(t)dtdot` Then (a)`f(0)<0` (b)`f(x)` is a decreasing function. (c)`f(x)` is an increasing function. (d)`int_0^1f(x)dx >0`

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A function f(x) satisfies f(x)=sinx+int_0^xf^(prime)(t)(2sint-sin^2t)dt is

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if ((d/(dx)f(x)))_(x=a)=b ,t h e n((d/(dx)f(x)))_(a+4000)=bdot Statement 2: f(x) is a periodic function with period 4.

Let f: RvecR be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) is______

If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3, then the value of f(-3) is ______________

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int_(0)^(x)(x-t)f^(')(t)dt The value of f(0)+f^(')(0) equal

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx in Rdot STATEMENT 1 : The possible least value of t for which int_a^(a+t)f(x)dx is independent of ai s12. STATEMENT 2 : f(x) is a periodic function.

y=f(x) satisfies the relation int_(2)^(x)f(t)dt=(x^(2))/2+int_(x)^(2)t^(2)f(t)dt The value of x for which f(x) is increasing is

f(x) satisfies the relation f(x)-lambdaint_0^(pi//2)sinx*costf(t)dt=sinx If lambda > 2 then f(x) decreases in