2x 4x 6x - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.3
Find the integrals of the functions in Exercises 62 to 83.

Question : 64 of 271

Marks: +1, -0

\cos 2x \cos 4x \cos 6x

Solution:

Let

I=\int \cos 2x \cos 4x \cos 6x dx

=\frac{1}{2}\int(2 \cos 2x \cos 4x)\cos 6x dx

=\frac{1}{2}\int( \cos 6x +\cos 2x )\cos 6x dx

[\because 2 \cos A \cos B = \cos (A+B) + \cos (A-B)]

=\frac{1}{4}\int 2\cos^2 6xdx+\frac{1}{4}\int(2\cos 2x\cos 6x)dx

=\frac{1}{4}\int(1+\cos 12x)dx+\frac{1}{4}\int(\cos 8x+\cos 4x)dx

=\frac{1}{4}x + \frac{1}{4}\left( \frac{\sin 12x}{12} \right) + \frac{1}{4}\left( \frac{\sin 8x}{8} + \frac{\sin 4x}{4} \right) + C

=\frac{1}{4}\left[ x + \frac{1}{12} \sin 12x + \frac{1}{8} \sin 8x + \frac{1}{4} \sin 4x \right] + C

Go to Question: