Let `f (x) = x – [x],` for every real number x, where `[x]` is the greatest integer less than or equal to x. Then, evaluate `int_-1^1 f(x) dx.`

Question

Let `f (x) = x – [x],` for every real number x, where `[x]` is the greatest integer less than or equal to x. Then, evaluate `int_-1^1 f(x) dx.`

Let `f (x) = x – [x],` for every real number x, where `[x]` is the greatest integer less than or equal to x. Then, evaluate `int_-1^1 f(x) dx.`
A. 1
B. 2
C. 3
D. 0

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
`int_(-1)^(1)(x-[x])dx=int_(-1)^(0)(x+1)dx+int_(0)^(1)(x-0)dx`
`=[(x^(2))/(2)+x]_(-1)^(0)+[(x^(2))/(2)]_(0)^(1)=(1)/(2)+(1)/(2)=1`

5 views Answered 2023-02-05 15:29