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Let [x] and {x} be the integer part and ...

Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral `int_(0)^(5)[x]{x}dx` is -

A

`5//2`

B

5

C

`34.5`

D

`35.5`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(0)^(5)[x]{x}dx=int_(0)^(5)[x](x-[x])dx=int_(0)^(1)0.dx+int_(1)^(2)1.(x-1)dx+int_(2)^(3)2(x-2)dx+int_(3)^(4)3(x-3)dx+int_(4)^(5)4(x-4)dx`
`(((x-1)^(2))/(2))^(2)+2(((x-2)^(2))/(2))_(2)^(3)+3(((x-3)^(2))/(2))_(3)^(4)+4(((x-4)^(2))/(2))_(4)^(5)`
`(1)/(2)+(2)/(2)+(3)/(2)+(4)/(2)`
= 5
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