Integrate sqrt((1-cos(x))/2) from 0 to 2π

[DorumonSg]

Erm, I have this integration question:

sqrt((1-cos(x))/2) with an upper limit of 2pie and lower limit of 0.

I can't seem to do it right.

I tried simplifying it:

sqrt((1-cos(x))/2)
= ((1-cos(x))/2)^(1/2)
= 1 - (cos^-2(x))^(1/2)
= 1 - cos^-1(x)

Then I intgrated 1... which becomes x, but I have no idea how to do cos^-1(x), I saw the long formula for the integration of cos^something(x) but I don't think it applies here... because the answer is 4...

 

[ChaoticLlama]

sqrt((1-cos(x))/2)
= ((1-cos(x))/2)^(1/2)
= 1 - (cos^-2(x))^(1/2)

bad.. BAD Dorumon! =P

sqrt(a + b) =/= a + sqrt(b)

You should have some trigonometric substitutions in your notes/textbook that involve cosine. Take a look at them, and see if they make the integrand a little nicer.