∫_ π/2^π/2√(1/2(1 cos 2x))dx= 2 ∫_0^π/2 |sin x|dx =2 [ cos x]^π/2_0=2 [ cos ( π/2 )+cos 0 ]=2 ...

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Second Fundamental Theorem of Calculus

∫-π/2π/2√1/21...

Question

$\int_{- \frac{π}{2}}^{\frac{π}{2}} \sqrt{\frac{1}{2} (1 - c o s 2 x)} d x =$

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\frac{1}{2}

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None of these

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Solution

The correct option is B
2

$\int_{- \frac{π}{2}}^{\frac{π}{2}} \sqrt{\frac{1}{2} (1 - c o s 2 x)} d x = 2 \int_{0}^{\frac{π}{2}} | s i n x | d x$
$= 2 [- c o s x]_{0}^{\frac{π}{2}} = 2 [- c o s (\frac{π}{2}) + c o s 0] = 2$

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