^4 2x - 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 : 72 of 271

Marks: +1, -0

\cos^4 2x

Solution:

Let

I=\int\cos^4 2xdx

=\int\left(\frac{1+\cos4x}{2}\right)^2dx

=\frac{1}{4}\int(1+\cos^2 4x+2\cos4x)dx

=\frac{1}{4}\int\left[1+\frac{1+\cos8x}{2}+2\cos4x\right]dx

=\frac{3}{8}\int dx+\frac{1}{8}\int\cos8xdx+\frac{1}{2}\int\cos 4xdx

=\frac{3}{8}x+\frac{1}{64}\sin8x+\frac{1}{8}\sin4x+C

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