Question Bank [2022] — Maths STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
$\int \sin 4 x \cos 3 x d x$
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Answer
$\text { Let } I =\int \sin 4 x \cdot \cos 3 x d x$
$=\frac{1}{2} \int(2 \sin 4 x \cdot \cos 3 x) d x$
$=\frac{1}{2} \int[\sin (4 x+3 x)+\sin (4 x-3 x)] d x \quad \ldots \ldots[\because 2 \sin A \cos B =\sin ( A + B )+\sin ( A - B )]$
$=\frac{1}{2} \int(\sin 7 x+\sin x) d x$
$=\frac{1}{2}\left[\int \sin 7 x d x+\int \sin x d x\right]$
$=\frac{1}{2}\left(\frac{-\cos 7 x}{7}-\cos x\right)+ c$
$\therefore I =-\frac{1}{14} \cos 7 x-\frac{1}{2} \cos x+ c $
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