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Integral Calculus> integrate the following integral ∫ cos^4 ...

question mark

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

taniska , 11 Years ago

Grade 12

2 Answers

Jitender Singh

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

$I = \int cos^{4}2xdx$
$I = \int cos^{2}2x.cos^{2}2xdx$
$I = \int cos^{2}2x(1-sin^{2}2x)dx$
$I = \int cos^{2}2xdx-\int cos^{2}2xsin^{2}2xdx$
$I = \frac{1}{2}\int 2cos^{2}2xdx-\frac{1}{4}\int 4cos^{2}2xsin^{2}2xdx$
$I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{4}\int (2sin2xcos2x)^2dx$
$I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{4}\int (sin4x)^2dx$
$I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{8}\int 2(sin4x)^2dx$
$I = \frac{1}{2}\int (1+cos4x)dx-\frac{1}{8}\int (1-cos8x)dx$
$I = \frac{1}{2}(x+\frac{sin4x}{4})-\frac{1}{8}(x-\frac{sin8x}{8})+c$

Last Activity: 11 Years ago

pavansai

i=∫cos⁴x

i=∫cos4x+1/2>²

i=1/4×∫1+cos²4x+2cos4x

i=1x/4 +1/4

i=1/2

Last Activity: 11 Years ago

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