First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} \tan^{- 1} \frac{2 x - 1}{1 + x - x^{2}} d x =$

Moderate

A

$\frac{π}{4}$
B

$\ln 2$
C

$\frac{π}{4} - \ln 2$
D

0

Solution

$I = \int_{0}^{1} \tan^{- 1} \frac{2 x - 1}{1 + x - x^{2}} d x, x \to 1 - x$
$I = \int_{0}^{1} \tan^{- 1} \frac{1 - 2 x}{1 + x - x^{2}} d x$

$2 I = 0 \to I = 0$

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