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

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

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

\int_{0}^{2 π} 1 + cos (θ) d θ

5.65685 \dots

Solution steps

\int_{0}^{2 π} 1 + cos (θ) d θ

Evaluating using numerical calculation methods

= 5.65685 \dots

\int_{- π}^{π} x cos^{2} (x) d x

\int_{0}^{1} x a x^{a - 1} d x

\int_{0}^{3} (9 - x^{2})^{\frac{3}{2}} d x

\int_{- 3}^{- 1} (2 t + 5) d t

\int_{- \infty}^{0} x e^{\frac{x}{2}} d x

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