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# Solution for ∫ 3 π 2 π √ 1 − Cos 2 X D X - CBSE (Science) Class 12 - Mathematics

ConceptProperties of Definite Integrals

#### Question

$\int_\pi^\frac{3\pi}{2} \sqrt{1 - \cos2x}dx$

#### Solution

$\int_\pi^\frac{3\pi}{2} \sqrt{1 - \cos2x}dx$
$= \int_\pi^\frac{3\pi}{2} \sqrt{2 \sin^2 x}dx$
$= \sqrt{2} \int_\pi^\frac{3\pi}{2} \left| \sin x \right|dx$
$= - \sqrt{2} \int_\pi^\frac{3\pi}{2} \sin x\ dx \left( \sin x < 0 for\ \pi \leq x \leq 2\pi \right)$

$= - \sqrt{2}\left( - \cosx \right) |_\pi^\frac{3\pi}{2}$
$= \sqrt{2}\left( \cos\frac{3\pi}{2} - cos\pi \right)$
$= \sqrt{2} \left[ 0 - \left( - 1 \right) \right]$
$= \sqrt{2} \times 1$
$= \sqrt{2}$

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Solution ∫ 3 π 2 π √ 1 − Cos 2 X D X Concept: Properties of Definite Integrals.
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