if `int_0^(x^2(1+x))f(t)dt=x` then the value of 10f(2) must be

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

If f(x)=x+int_0^1t(x+t)f(t) dt ,then the value of 23/2f(0) is equal to _________

If int_[x]^(x+1) f(t)dt =[x] then th value of int_(-2)^4 f(x) dx is equal

Newton-Leinbnitz's formula states that d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)} Answer the following questions based on above passage: Let f(x) be a differentiable function and f(1)=2, If lim_(xrarr1)int_2^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is equal to

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt , then the value of (23)/(3)f(0) is equal to-

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) 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

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

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 T le0 be a fixed real number suppose f is continuous function such that for all x in R f(x+T)=F(x) if I=int_0^T f(x)dx then the value of int_3^(3+3T)f(2x)dx is