integration of (1-cosx)^1/2
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Hiiiii.....
Note that, by the cosine double-angle formula:
cos(2x) = 1 - 2sin^2(x):
By solving this for 2sin^2(x):
2sin^2(x) = 1 - cos(2x).
If we replace x with x/2, we get:
2sin^2(x/2) = 1 - cos(x).
Therefore:
∫ √[1 - cos(x)] dx
= ∫ √[2sin^2(x/2)] dx, from above
= √2 ∫ sin(x/2) dx
= -2√2*sin(x/2) + C.
I hope this helps!
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Note that, by the cosine double-angle formula:
cos(2x) = 1 - 2sin^2(x):
By solving this for 2sin^2(x):
2sin^2(x) = 1 - cos(2x).
If we replace x with x/2, we get:
2sin^2(x/2) = 1 - cos(x).
Therefore:
∫ √[1 - cos(x)] dx
= ∫ √[2sin^2(x/2)] dx, from above
= √2 ∫ sin(x/2) dx
= -2√2*sin(x/2) + C.
I hope this helps!
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