What is the integral from 0 to 2pi of sqrt(1+cos(x)) ?

The integral from 0 to 2pi of sqrt(1+cos(x)) is 5.65685…

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integral from 0 to 2pi of sqrt(1+cos(x))

\int_{0}^{2 π} 1 + cos (x) d x

5.65685 \dots

Solution steps

\int_{0}^{2 π} 1 + cos (x) d x

Evaluating using numerical calculation methods

= 5.65685 \dots

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\int_{0}^{2 π} cos^{2} (θ) sin (θ) d θ

\int_{- π}^{π} e^{x} cos (x) d x

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What is the integral from 0 to 2pi of sqrt(1+cos(x)) ?
The integral from 0 to 2pi of sqrt(1+cos(x)) is 5.65685…