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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
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

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