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Integral of ((1-cos(2x))^0.5) dx

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The solution

You have entered [src]
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$$\int\limits_{0}^{1} \sqrt{- \cos{\left(2 x \right)} + 1}\, dx$$
Integral(sqrt(1 - cos(2*x)), (x, 0, 1))
The answer (Indefinite) [src]
$${{\left(-\sqrt{2}\,\cos \left(2\,x\right)-\sqrt{2}\right)\,\sin \left({{{\rm atan2}\left(\sin \left(2\,x\right) , \cos \left(2\,x \right)\right)+\pi}\over{2}}\right)+\sqrt{2}\,\sin \left(2\,x\right) \,\cos \left({{{\rm atan2}\left(\sin \left(2\,x\right) , \cos \left( 2\,x\right)\right)+\pi}\over{2}}\right)}\over{2}}$$
The answer [src]
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$${{-\sqrt{2}\,\sin 2\,\cos \left({{\arctan \left({{\sin 2}\over{ \cos 2}}\right)}\over{2}}\right)+\sqrt{2}\,\cos 2\,\cos \left({{ \arctan \left({{\sin 2}\over{\cos 2}}\right)}\over{2}}\right)+\sqrt{ 2}\,\cos \left({{\arctan \left({{\sin 2}\over{\cos 2}}\right)}\over{ 2}}\right)+2^{{{3}\over{2}}}}\over{2}}$$
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$$\int\limits_{0}^{1} \sqrt{- \cos{\left(2 x \right)} + 1}\, dx$$
Numerical answer [src]
0.650110713632916
0.650110713632916

    Use the examples entering the upper and lower limits of integration.