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)=

Find f(x) if it satisfies the relation f(x) = e^(x) + int_(0)^(1) (x+ye^(x))f(y) dy .

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

Let f: R to R be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) 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 (a) -1 (b) 0 (c) 1 (d) none of these

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 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…………………..

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then Number of roots of the equation f(x)=e^(x) is

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.