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Integral Calculus> evaluate ∫ (cos^2(x) – sin^2(x)) / sqrt(1...

question mark

evaluate
∫ (cos^2(x) – sin^2(x)) / sqrt(1 + cos 4x) dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

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

$I = \int \frac{cos^{2}x-sin^{2}x}{\sqrt{1+cos4x}}dx$
$I = \int \frac{cos^{2}x-sin^{2}x}{\sqrt{2cos^{2}2x}}dx$
$I = \frac{1}{\sqrt{2}}\int \frac{cos^{2}x-sin^{2}x}{cos2x}dx$
$I = \frac{1}{\sqrt{2}}\int \frac{cos2x}{cos2x}dx$
$I = \frac{1}{\sqrt{2}}\int dx$
$I = \frac{x}{\sqrt{2}} + c$

Last Activity: 11 Years ago

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