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Let f (x) = x – [x], for every real numb...

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.`

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Text Solution

Verified by Experts

The correct Answer is:
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`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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