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Evaluate: ∫ 2 − 1 | X | X D X . - Mathematics

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प्रश्न

Evaluate:  `int_-1^2 (|"x"|)/"x"d"x"`.

योग
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उत्तर

`|"x"| = "x"  "when"  "x" ≥0`

= `-"x"  "when"  "x" < 0`

Therefore, `|"x"|/"x"` = 1 when x ≥ 0

= -1 when x < 0

Thus, `int_-1^2 |"x"|/"x"d"x" = int_-1^0 (-1)d"x" + int_0^2 (1)d"x"`

= `-1 xx ["x"]_1^0 + ["x"]_0^2`

= `(-1) [0 + 1] + [2 - 0] = -1 + 2 = 1`.

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2018-2019 (March) 65/1/3

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