`int_(-2)^(2)xdx-int_(-2)^(2)[x]dx`, जहाँ `[*]` अधिकतम पूर्णांक फलन है ,किसके बराबर है ?

Options

A. 0
B. 1
C. 2
D. 4

Answer

C

Explanation

`int_(-2)^(2)xdx-int_(-2)^(2)[x]dx`
दिया है, `[x]={{:(-2",",-2lexlt-1),(-1",",-1lexlt0),(0",",0lexlt1),(1",",1lexlt2):}`
`thereforeint_(-2)^(2)xdx=int_(-2)^(2)[x]dx`
`=0-[{:(int_(-2)^(-1)(-2)dx+int_(-1)^(0)(-1)dx,),(" "+int0dx+int_(1)^(2)1dx,):}]`
`=0-[-2(x)_(-2)^(-1)+(-x)_(-1)^(0)+(x)_(1)^(2)]`
`[becauseint_(-a)^(a)f(x)dx=0," यदि f(x) विषम हो" ]`
`=-[-2(-1+2)+(0-1)+(2-1)]`
`=-[-2-1+1]`
=2