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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{5}{7} $$\sin (3x+7) \cos (3x+7) dx$

$(a)\;\frac{-5}{84} \sin (6x+14)+c \\(b)\;\frac{-5}{84} \cos (6x+14)+c\\(c)\;\frac{-5}{21} \sin (6x+14)+c \\ (d)\;None$

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1 Answer

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By $\sin 2 \theta = 2 \sin \theta \cos \theta $
$\large\frac{5}{14} $$\int \sin (6x+14) dx$
=> $\large\frac{-5}{14} \frac{\cos(6x+4)} {6}+c$
=>$\large\frac{-5}{84} $$\cos (6x+14)+c$
Hence b is the correct answer.
answered Jan 2, 2014 by meena.p
 
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