11 авг. 2017 г. · it follows that the volume of the sphere is V=∫baπ[f(x)]2dx=∫r−rπ(r2−x2)dx=π[r2x−x33]=43πr3. Volume of a sphere using Calculus - Math Stack Exchange Triple integration for the volume of a given sphere Deriving the formula of the volume of a sphere using integration Другие результаты с сайта math.stackexchange.com

The sphere of radius r can be obtained rotating the half circle graph of the function y = p r − x2, x ∈ [−r, r]. about the x-axis. The volume V is obtained as ...

From the equation of the circle x2 + y2 = r2; x2 = r2 - y2.

We can calculate the volume of the sphere by integrating the areas of the discs from the lowest height of the sphere to the highest height of the sphere.

Продолжительность: 4:00
Опубликовано: 23 окт. 2017 г.

18 сент. 2014 г. · Since a sphere with radius r can be obtained by rotating the region bounded by the semicircle y=√r2−x2 and the x-axis about the x-axis, ...

Продолжительность: 6:24
Опубликовано: 8 мая 2021 г.

To find the volume of a sphere using integration first parameterize the equation of a circle. Next, use one of the three common methods for integrating solids ...

14 сент. 2023 г. · In this way the whole integral should represent 1/2 of the spheres volume and can be multiplied by two to get the full volume.

The volume of a sphere in three dimensions is given by the triple integral: V = ∭ V d V where V is the volume of the sphere. For a sphere with radius R , making ...