Let `f:R -(0,oo) ` be a real valued function satisfying `int_0^1 tf(x-t) dt =e^(2x)-1` then which of the following is/are correct?

Let f:R -(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then f(x) is

Let f:R ->(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then find f(x) ?

Let f:R ->(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then find f(x) ?

Let f be a continuous function on R and satisfies f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt, then which of the following is(are) correct?

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Let f be a real valued function defined on the interval (0,oo) by f(x)=In x+int_(0)^(x)sqrt(1+sint)dt . Then which of the following statement (s) is (are) true?