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integrate the following integral ∫ cos^4 (2x) dx

 
integrate the following integral
∫ cos^4 (2x) dx

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int cos^{4}2xdx
I = \int cos^{2}2x.cos^{2}2xdx
I = \int cos^{2}2x(1-sin^{2}2x)dx
I = \int cos^{2}2xdx-\int cos^{2}2xsin^{2}2xdx
I = \frac{1}{2}\int 2cos^{2}2xdx-\frac{1}{4}\int 4cos^{2}2xsin^{2}2xdx
I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{4}\int (2sin2xcos2x)^2dx
I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{4}\int (sin4x)^2dx
I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{8}\int 2(sin4x)^2dx
I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{8}\int (1-cos8x)dx
I = \frac{1}{2}(x+\frac{sin4x}{4})-\frac{1}{8}(x-\frac{sin8x}{8})+c
pavansai
20 Points
9 years ago
i=∫cos4x
i=∫cos4x+1/2>2
i=1/4×∫1+cos24x+2cos4x
i=1x/4   +1/4
i=1/2

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