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Question

Question: The integral <img src="https://cdn.pureessence.tech/canvas_47.png?top_left_x=1684&top_left_y=874&wid...

The integral equals -

A

– 12\frac { 1 } { 2 }

B

0

C

1

D

2 ln (12)\left( \frac { 1 } { 2 } \right)

Answer

– 12\frac { 1 } { 2 }

Explanation

Solution

∫−1/21/2[x]+In⁡∣1+x1−x∣\int _ { - 1 / 2 } ^ { 1 / 2 } [ x ] + \operatorname { In } \left| \frac { 1 + x } { 1 - x } \right| = ∫−1/21/2[x]\int _ { - 1 / 2 } ^ { 1 / 2 } [ x ] +0

= = (−1)01/2( - 1 ) _ { 0 } ^ { 1 / 2 } =−12- \frac { 1 } { 2 }