If `|f(x)-f(y)|le2|x-y|^((3)/(2))` `AAx,yinR` and `f(0)=1` then value of `int_(0)^(1)f^2(x)dx` is equal to (a) 1 (b) 2 (c) `sqrt2` (d) 4

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

If f(0)=1,f(2)=3,f'(2)=5 ,then find the value of I_(1)=int_(0)^(1)xf''(2x)dx

If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int_(0)^(1)x. f^''(2x) dx is equal to

The differentiable function y= f(x) has a property that the chord joining any two points A (x _(1), f (x_(1)) and B (x_(2), f (x _(2))) always intersects y-axis at (0,2 x _(1) x _(2)). Given that f (1) =-1. then: int _(0)^(1//2) f (x) dx is equal to : (a) 1/6 (b) 1/8 (c) 1/12 (d) 1/24

If int_(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x) , then int_(0)^(1)f^(')(x) dx is equal to

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

Let f(x)=int _( x )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integral int _(0)^(2) xf (x ) dx is equal to:

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

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to