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Integral Calculus> integrate the following integral ∫ cos x ...

question mark

integrate the following integral
∫ cos x cos 2x cos 3x dx

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int cosx.cos2x.cos3xdx$
$I = \int (cosx.cos3x).cos2xdx$
$I = \frac{1}{2}\int (cos2x+cos4x).cos2xdx$
$I = \frac{1}{2}\int (cos^{2}2x+cos4xcos2x)dx$
$I = \frac{1}{2}\int cos^{2}2xdx+\frac{1}{2}\int cos4xcos2xdx$
$I = \frac{1}{4}\int (1+cos4x)dx+\frac{1}{4}\int (cos2x+cos6x)dx$
$I = \frac{1}{4}(x+\frac{sin4x}{4})+\frac{1}{4}\int (cos2x+cos6x)dx$
$I = \frac{1}{4}(x+\frac{sin4x}{4})+\frac{1}{4}(\frac{sin2x}{2}+\frac{sin6x}{6})+c$
$I = \frac{1}{4}(x+\frac{sin4x}{4}+\frac{sin2x}{2}+\frac{sin6x}{6})+c$

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