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.`

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

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to

If f(x) = int_(0)^(x) t cos t dt , then (df)/(dx)

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If int_0^1(e^t)/(1+t)dt=a , then find the value of int_0^1(e^t)/((1+t)^2)dt in terms of a .