Matematika/Gauso formulė: Skirtumas tarp puslapio versijų

:<math>=3\int_0^{2\pi}d\phi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos\theta d\theta \frac{\rho^5}{5}|_0^R =3\cdot \frac{R^5}{5}\int_0^{2\pi}d\phi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos\theta d\theta = \frac{3 R^5}{5}\int_0^{2\pi}d\phi \; \sin\theta|_{-\frac{\pi}{2}}^{\frac{\pi}{2}} =\frac{3 R^5}{5}\int_0^{2\pi}( \sin\frac{\pi}{2}-\sin\frac{-\pi}{2})d\phi =</math>

:<math>=\frac{3 R^5}{5}\int_0^{2\pi}( 1-(-1))d\phi =\frac{6 R^5}{5}\phi|_0^{2\pi} =\frac{6 R^5}{5}\cdot 2\pi=\frac{12\pi R^5}{5}.</math>

:<math>x^2=R^2-y^2-z^2,</math>

:<math>x=\sqrt{R^2-y^2-z^2} ;</math>