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Question: The integral ![](https://cdn.pureessence.tech/canvas_568.png?top_left_x=600&top_left_y=1831&width=30...

The integral dx equals –

A

–1/2

B

0

C

1

D

2 log (1/2)

Answer

–1/2

Explanation

Solution

dx = ∫−1/21/2[x]dx\int _ { - 1 / 2 } ^ { 1 / 2 } [ x ] d x

(since log is an odd function)

= ∫−1/20(−1)\int _ { - 1 / 2 } ^ { 0 } ( - 1 ) dx = –12\frac { 1 } { 2 }.