-0-7sin 2 2 xdx is equal toA- 0B- -4C- -2D- -8

The correct option is D π8I=∫_0^π/4sin^2 2x dx Using property of integration nbsp; ⇒ I=∫_0^π/4sin^2 (π/2 x ) dx....(i) ⇒ I=∫_0^π/4cos^2 (π/2 x ) dx....(ii) ...

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Byju's Answer

Standard XII

Mathematics

Property 3

∫0π/7sin 2 2 ...

Question

$\frac{π}{4} \int 0 {sin}^{2} 2 x d x$ is equal to

0

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\frac{π}{2}

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\frac{π}{4}

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\frac{π}{8}

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Solution

The correct option is D $\frac{π}{8}$
$I = \frac{π}{4} \int 0 {sin}^{2} 2 x d x$
Using property of integration
$\Rightarrow I = \frac{π}{4} \int 0 {sin}^{2} (\frac{π}{2} - x) d x . . . . (i)$
$\Rightarrow I = \frac{π}{4} \int 0 {cos}^{2} (\frac{π}{2} - x) d x . . . . (i i)$
Adding $(i)$ and $(i i)$ , we get:
$2 I = \frac{π}{4} \int 0 1 d x$
$I = \frac{π}{8}$

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