# 1 ∫ 0 1 − X 1 + X D X - Mathematics

Sum

$\int\limits_0^1 \frac{1 - x}{1 + x} dx$

#### Solution

$\int_0^1 \frac{1 - x}{1 + x} dx$

$= \int_0^1 \frac{1 - x - 1 + 1}{1 + x} d x$

$= \int_0^1 \frac{2 - \left( x + 1 \right)}{1 + x} d x$

$= \int_0^1 \frac{2}{1 + x} - \int_0^1 \frac{1 + x}{1 + x}dx$

$= \int_0^1 \frac{2}{1 + x} - \int_0^1 dx$

$= 2 \left[ \log\left( 1 + x \right) \right]_0^1 - \left[ x \right]_0^1$

$= 2\log2 - 1$

Concept: Definite Integrals Problems
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 20 Definite Integrals
Revision Exercise | Q 9 | Page 121