The correct option is B log 2 ∫_0^π2cos #160; #10;x1+sin #160; xdx #10;we know that #10; ∫_0^π2cos #160; x1+sin #160; #10;xdx=∫_ ...

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Integration Using Substitution

∫0π/2cos x/1+...

Question

$\int_{0}^{π_{/} 2} \frac{cos x}{1 + sin x} d_{X =}$

log 2

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log e

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\frac{1}{2}

log3

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0

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Solution

The correct option is B $log 2$
$\int_{0}^{\frac{π}{2}} \frac{c o s x}{1 + s i n x} d x$
we know that
$\int_{0}^{\frac{π}{2}} \frac{c o s x}{1 + s i n x} d x = \int_{0}^{\frac{π}{2}} \frac{d (s i n x)}{1 + s i n x}$
$\int_{0}^{\frac{π}{2}} \frac{d (s i n x)}{1 + s i n x} = l o g (1 + s i n x) \int_{0}^{\frac{π}{2}}$
$= l o g (1 + s i n \frac{π}{2}) - l o g (1 + s i n 0)$
$= l o g (2)$
$= l o g 2$

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Similar questions

π / 2 \int 0 \frac{cos x}{1 + cos x + sin x} d x

\int_{0}^{π / 2} \frac{cos x}{(1 + sin x) (2 + sin x)} d x

\int_{0}^{\frac{π}{2}} \frac{c o s x}{(1 + s i n x) (2 + s i n x)} d x =

\int_{0}^{π / 2} \frac{cos x}{(1 + sin x) (2 + sin x)} d x

{log}_{2} x, {log}_{3} x, {log}_{e} x, {log}_{4} x

x > 1

0 < x < 1

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