calculate : $\displaystyle \int_{0}^{2\pi }\sqrt{\frac{1+cos\left (x \right )}{2}}dx$
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it is equal to 4. get out of the root the square root of 2 and then use the half angle formula for cosx...the rest is easy.
Why would you take out $\displaystyle \displaystyle \begin{align*} \sqrt{2} \end{align*}$? It can already be turned into a half-angle and does not have any constant multiples...
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