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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

The value of ∫_0^ 2π ^ -1 ( (1 - ^2 (x)/(2))/(1 + ^2 (x)/(2)) ) dx...

The value of

\int_0^{2\pi} \cos^{-1} \left( \frac{1 - \tan^2 \frac{x}{2}}{1 + \tan^2 \frac{x}{2}} \right) dx

is :

Options

A $\pi^2$
B $\frac{\pi^2}{2}$
C $2\pi^2$
D $\pi^3$

Correct answer

D. $\pi^3$

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