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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \sqrt {1+\sin x }dx$

$(a)\;-2 \cos (\frac{x}{2}) +2 \sin \frac{x}{2}+c \\(b)\;\sin \frac{x}{2}+ \cos \frac{x}{2}+c \\(c)\;-\tan (\frac{x}{2}) + \cot \frac{x}{2}+c \\ (d)\;None$
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1 Answer

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=> $ \int \sqrt {\sin^2 \large\frac{x}{2} +\cos ^2 \large\frac{x}{2} + 2 \sin \large\frac{x}{2} \cos \large\frac{x}{2}}$$dx$
=> $\int (\sin \large\frac{x}{2}$$+ \cos \large\frac{x}{2})$$dx$
$-2 \cos (\large\frac{x}{2}$$) +2 \sin \large\frac{x}{2}$$+c$
Hence a is the correct answer.
answered Dec 30, 2013 by meena.p
 
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