Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

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