0-pi-1-cos-2-x-dx-

Question Number 186181 by cortano1 last updated on 02/Feb/23

\underset{0}{\int^{π}} \sqrt{1 + \cos^{2} x} d x = ?

Answered by MJS_new last updated on 02/Feb/23

\int \sqrt{1 + \cos^{2} x} d x = \int \sqrt{2 - \sin^{2} x} d x =

= \sqrt{2} \int \sqrt{1 - \frac{1}{2} \sin^{2} x} d x = \sqrt{2} E (x ∣ \frac{1}{2}) + C

not sure if we can give an exact value \dots

\sqrt{2} {[E (x ∣ \frac{1}{2})]}_{0}^{π} \approx 3.82019778903

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