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int(-1)^(1)x|x|dx is equal to...

`int_(-1)^(1)x|x|dx` is equal to

A

`2`

B

`1`

C

`1/4`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x) = x|x|`
`f(-x) = -x|-x| =-x| x| = - f(x)`
`rArr x|x|` is in an odd function.
Hence, `int_(-1)^(1)x|x|dx = 0`
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NDA PREVIOUS YEARS-DEFINITE INTEGRATION & ITS APPLICATION-DIRECTIONS
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