Integral Calculus Question 107

Question: $ \int_{{}}^{{}}{\sqrt{1-\sin 2x}\ }dx=……..,\ \ x\in (0,\ \pi /4) $

[MP PET 1987]

Options:

A) $ -\sin x+\cos x $ + C

B) $ \sin x-\cos x $ + C

C) $ \tan x+\sec x $ + C

D) $ \sin x+\cos x $ + C

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Answer:

Correct Answer: D

Solution:

$ \int_{{}}^{{}}{\sqrt{1-\sin 2x}}dx $ $ =\int_{{}}^{{}}{(\cos x-\sin x)dx=\sin x+\cos x+c.} $