- 0 - - 21-cos 2 x d x

#8747;0 #960;21 cos2xdx= #8747;0 #960;22sin2x #160; #160;dx #160;= #8747;0 #960;22 #160;sinx #160; #160;dx= 2 #160;cosx0 #960;2= 0 ...

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Property 7

∫ 0 π / 21-co...

Question

$\int_{0}^{π / 2} \sqrt{1 - \cos 2 x} d x .$

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Solution

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\int_{0}^{\frac{π}{2}} \frac{1}{1 + {cos}^{2} x} d x

\frac{π}{2} \int 0 \frac{1}{a^{2} . {sin}^{2} x + b^{2} . {cos}^{2} x} d x

\int_{0}^{π / 2} \frac{1}{a^{2} . s i n^{2} x + b^{2} . c o s^{2} x} d x

I_{1} = \int_{0}^{\frac{π}{2}} \frac{{cos}^{2} x}{1 + {cos}^{2} x} d x,

I_{2} = \int_{0}^{\frac{π}{2}} \frac{{sin}^{2} x}{1 + {sin}^{2} x} d x,

I_{3} = \int_{0}^{\frac{π}{2}} \frac{1 + 2 {cos}^{2} x {sin}^{2} x}{4 + 2 {cos}^{2} x {sin}^{2} x} d x

a_{n} = \int_{0}^{π / 2} \frac{1 - c o s 2 n x}{1 - c o s 2 x} d x,

∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{π}{2} & a_{2} & a_{3} a_{4} & a_{5} & a_{6} a_{7} & a_{8} & a_{9} \end{matrix} ∣ ∣ ∣ ∣ ∣

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