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UPSC NDA II 2015 Mathematics Solved Paper

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For the next two(2) items that follow:

Consider the integrals

A=\int\limits_{0}^{\pi} \;\frac{\sin x \, d x}{\sin x+\cos x}

and

B=\int\limits_{0}^{\pi} \;\frac{\sin x \, d x}{\sin x-\cos x}

[NDA II 2015]

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Question : 97 of 120

Marks: +1, -0

Which one of the following is correct ?

$A = 2B$
$B = 2A$
$A = B$
$A = 3B$

Solution:

A = \int\limits_{0}^{\pi} \frac{\sin x}{\sin x + \cos x} \, dx

Using property (iv)

A = \int\limits_{0}^{\pi} \frac{\sin(\pi - x)}{\sin(\pi - x) + \cos(\pi - x)} \, dx

A \int\limits_{0}^{\pi} \frac{\sin x}{\sin x - \cos x} \, dx = B

A = B

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