The correct option is C 0 Let I = #10;∫_0^100π√(1 cos 2x) dx #10; #10; I = ∫_0^100π #10;√(2sin^2x) dx #10; #10; = ∫_0^100π # ...

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

∫0100 π√1-cos...

Question

$\int_{0}^{100 π} \sqrt{1 - cos 2 x} d x$ is

200 \sqrt{2}

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100 \sqrt{2}

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Solution

The correct option is C $0$
Let $I = 100 π \int 0 \sqrt{1 - cos 2 x} d x$

$I = 100 π \int 0 \sqrt{2 {sin}^{2} x} d x$

$= 100 π \int 0 \sqrt{2} sin x d x$

$= - \sqrt{2} {[cos x]}_{0}^{100 π}$

$= - \sqrt{2} (cos 100 π - cos 0)$

$= - \sqrt{2} (1 - 1)$

$= 0$

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