Matematika/Gauso formulė: Skirtumas tarp puslapio versijų
Ištrintas turinys Pridėtas turinys
79 eilutė:
:Taikydami formulę Gauso, gauname:
:<math>\iint_S x^2 dy dz=\iiint_V(2x+0+0)dx dy dz=2\int_0^{2\pi}d\phi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos\theta d\theta\int_0^R\rho^3 d\rho=</math>
:<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>
==Taip pat skaitykite==
| |||