Oblicz pole figury

[kotekvg]

obliczyc pole figury powstalem przez obrot sinusoidy y=sin x 0

[luka52]

\(\displaystyle{ S = 2 \pi \int\limits_0^{\pi} y \sqrt{1 + \left( \frac{dy}{dx} \right)^2} \, = 2 \pi \int\limits_0^{\pi} \sin x \sqrt{1 + \cos^2 x} \, = \\ =- \pi \mbox{arcsinh} \, (\cos x) - \pi \cos x \sqrt{1+ \cos^2 x} \Big|_0^{\pi} = \sqrt{2} + \ln (1 + \sqrt{2})}\)