Mathematics

Obtain $$ \displaystyle \int _{ 0 }^{ \pi  }{ \sqrt { 1+\cos { 2x }  } dx } $$


ANSWER

$$0$$


SOLUTION
$$\displaystyle\int^{\pi}_0\sqrt{1+\cos^2x}dx$$
$$\cos 2x=2\cos^2x-1$$
$$\displaystyle\int^{\pi}_0\sqrt{1+2\cos^2x-1}dx$$
$$\displaystyle\int^{\pi}_0\sqrt{2}\cos xdx$$
$$=\sqrt{2}[\sin x]^{\pi}_0$$
$$=\sqrt{2}[0-0]$$
$$=0$$.
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Single Correct Medium Published on 17th 09, 2020
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