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Indefinite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration2 Marks
Question
Evaluate:
$\int \cos ^2 x \cdot d x$
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Answer

Recall the identity $\cos 2 x=2 \cos ^2 x-1$,
which gives$\cos ^2 x=\frac{1+\cos 2 x}{2}$
Therefore, $\int \cos ^2 x \cdot d x$
$=\frac{1}{2} \int(1+\cos 2 x) \cdot d x$
$=\frac{1}{2} \int d x+\frac{1}{2} \int \cos 2 x \cdot d x$
$=\frac{x}{2}+\frac{1}{4} \sin 2 x+C .$

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