MCQ
$\int {\left( {\sin x\cos x\cos 2x\cos 4x\cos 8x} \right)dx}$ equal
  • A
    $\frac{{ - 1}}{{128}}\cos 16x + C$
  • B
    $\frac{{1}}{{256}}\cos 16x + C$
  • C
    $\frac{{ - 1}}{{256}}\sin 16x + C$
  • $\frac{{ - 1}}{{256}}\cos 16x + C$

Answer

Correct option: D.
$\frac{{ - 1}}{{256}}\cos 16x + C$
d
$I = \frac{1}{2}\int {\sin } \,2x\cos \,2x\cos \,4x\cos \,8x\,dx$

$ = \frac{1}{4}\int {\sin } \,4x\cos \,4x\cos \,8x\,dx$

$ = \frac{1}{8}\int {\sin } \,8x\cos \,8x\,dx = \frac{1}{{16}}\int {\sin } \,16x\,dx$

$=\frac{-1}{256} \cos 16 x+C$

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