Suppose f is continuous, `f(0)=0,f(1)=1,f^(prime)(x)>0"and"int_0^1f(x)dx=1/3,` Find the value of the definite integral `int_0^1f^-1(y)dy.`

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)=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)=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)=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(0)=1,f(2)=3,f'(2)=5 ,then the value of the definite integral int_(0)^(1)xf''(2x)dx is

If f(0)=1 , f(2)=3 , f'(2)=5 , then the value of the definite integral int_0^(1)xf''(2x)dx is _________

Let f(x) be a continuous function on [0,4] satisfying f(x)f(4-x)=1. The value of the definite integral int_(0)^(4)(1)/(1+f(x))dx equals -

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

Suppose f,f' and f" are continuous on [0,e] and that f^(prime)(e)=f(e)=f(1)=1 and int_1^e(f(x))/(x^2)dx=1/2, then the value of int_1^0 f*(x)ln xdx equals.

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is