Home
Class 12
MATHS
If int0^x[x]dx=int0^([x])xdx , then pro...

If `int_0^x[x]dx=int_0^([x])xdx ,` then prove that either `x` is purely fractional or `x` is such that `{x}=1/2(w h e r e[dot]a n d{dot}` denote the greatest integer and fractional part, respectively).

Promotional Banner

Similar Questions

Explore conceptually related problems

If int_(0)^(x)[x]dx=int_(0)^([x])xdx, then prove that either x is purely fractional or x is such that {x}=(1)/(2)(where[.]and{.} denote the greatest integer and fractional part,respectively).

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

If int_(0)^(x)[x]dx=int_(0)^(|x|)x dx, (where [.] and {.} denotes the greatest integer and fractional part respectively), then

The value of int_(0)^(|x|){x} dx (where [*] and {*} denotes greatest integer and fraction part function respectively) is