Matematika/Gauso formulė: Skirtumas tarp puslapio versijų

:<math>=2\int_0^{2\pi}d\phi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos\theta d\theta \frac{\rho^4}{4}|_0^R =2\cdot \frac{R^4}{4}\int_0^{2\pi}d\phi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos\theta d\theta = \frac{R^4}{2}\int_0^{2\pi}d\phi \; \sin\theta|_{-\frac{\pi}{2}}^{\frac{\pi}{2}} =\frac{ R^4}{2}\int_0^{2\pi}( \sin\frac{\pi}{2}-\sin\frac{-\pi}{2})d\phi =</math>

:<math>=\frac{ R^4}{2}\int_0^{2\pi}( 1-(-1))d\phi =R^4\phi|_0^{2\pi} = R^4\cdot 2\pi=2\pi R^4.</math>

 

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