The correct option is A 2√(1+sin x)+C I=∫√(1 sinx)dx =∫√(1 sinx×(1+sinx/1+sinx))dx =∫√((1^2 sin^2x/1+sinx))dx =∫(cosx/√(1+sinx))dx let 1 ...

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Integration of Trigonometric Functions

∫√ 1 - sin x ...

Question

$\int \sqrt{1 - sin x} d x =$

2 \sqrt{1 + sin x} + C

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2 \sqrt{1 - sin x} + C

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2 \sqrt{1 - 2 sin x} + C

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2 \sqrt{1 - sin 2 x} + C

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Solution

The correct option is A $2 \sqrt{1 + sin x} + C$
$I = \int \sqrt{1 - s i n x} d x = \int \sqrt{1 - s i n x \times (\frac{1 + s i n x}{1 + s i n x})} d x$
$= \int \sqrt{(\frac{1^{2} - s i n^{2} x}{1 + s i n x})} d x = \int (\frac{c o s x}{\sqrt{1 + s i n x}}) d x$
let 1+sinx=t
then cosx dx=dt
$o r I = \int (\frac{1}{\sqrt{t}}) d t$
$= (\frac{t^{(} \frac{1}{2})}{(\frac{1}{2})}) + C 2 \sqrt{1 + s i n x} + C$

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