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Integral Calculus> evaluate the following integral ∫ sqrt((1...

question mark

evaluate the following integral
∫ sqrt((1 – sin 2x) / (1 + sin 2x)) dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:
Hello student,
Please find the answer to your question below

$I = \int \sqrt{\frac{1-sin2x}{1+sin2x}}dx$
$I = \int \sqrt{\frac{sec2x-tan2x}{sec2x+tan2x}}dx$
$I = \int \sqrt{\frac{(sec2x-tan2x)(sec2x+tan2x)}{(sec2x+tan2x)(sec2x+tan2x)}}dx$
$I = \int \sqrt{\frac{(sec^{2}2x-tan^{2}2x)}{(sec2x+tan2x)^2}}dx$
$I = \int \frac{1}{sec2x+tan2x}dx$
$I = \int \frac{cos2x}{1+sin2x}dx$
$1+sin2x = t$
$2cos2xdx = dt$
$I = \frac{1}{2}\int \frac{dt}{t}$
$I = \frac{logt}{2} + c$
$I = \frac{log(1+sin2x)}{2} + c$

Last Activity: 11 Years ago

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