The value of \int_{0}^{\pi \/ 4}( \sin 2 x) \dx is:

CBSE Class 12 Math 2023 Delhi Set 2 Solved Paper

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Question : 4 of 14

Marks: +1, -0

The value of

∫↙{0}↖{π \/ 4}( sin \;2 x) \dx

is:

0
$\;{1}/{2}$
1
$-\;{1}/{2}$

Solution:

Explanation:

∫↙{0}↖{π \/ 4} sin \;2 x \dx

Let

\;\; u=2 x

If

x=0

then,

u=0

\;\text " and "\; x=π \/ 4 \;\text " then "\; u=π \/ 2 \;\text ". "\;

⇒ \;\; d u=2 \dx

\;{1}/{2} ∫↙{0}↖{π \/ 2} \sin \;u \du=-\;{1}/{2}[\cos u]_0^{π \/ 2}

=-\;{1}/{2}[0-1]=\;{1}/{2}

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