integrating by eliminating square root?

Question

integrate

sqrt(1 - cos 2x) dx

how would I solve this integration by eliminating the square root? can anybody help me with this?

Thanks

Answer 1

since cos2x= 1-2sin^2(x)

so 1-cos2x = 2sin^2(x)

and sqrt(1-cos2x) = sqrt(2sin^2(x))
=sqrt(2) * sinx

say y = sqrt(2) * sinx

so integral of y = sqrt(2) -cosx { because integral of sinx is -cosx}

hence ur answer is -sqrt(2)*cosx

Answer 2

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1. integral = int cos(x)dx = sinx + c 2. integral = int sec(x) dy = ln(secx + tanx) + c

Answer 3

1-cos2x = 1-(2cos^2(x)-1) = -2cos^2(x)
So sqrt(1-cos2x) = sqrt(-2) cos(x); treat sqrt(-2) as a constant.

Answer 4

∫√(1 - cos2x) dx

= ∫√(1- ( 1 - 2sin² x)) dx

= ∫√(2sin² x) dx

= ∫√2 .sin x dx

= -√2cosx + c

Answer 5

Here is the answer:
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