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. Triple integration for the volume of a given sphere integration - Volume of a sphere using cartesian coordinates Другие результаты с сайта math.stackexchange.com

A Sphere. The equation for the outer edge of a sphere of radius a is given by x2 + y2 + z2 = a2. If we want to consider the volume inside, then we are ...

16 нояб. 2022 г. · In this section we will look at converting integrals (including dV) in Cartesian coordinates into Spherical coordinates.

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. Comprehensive Look at... · Exploring Volume Integral...

31 мая 2019 г. · We can use triple integrals and spherical coordinates to solve for the volume of a solid sphere. To convert from rectangular coordinates to ...

9 нояб. 2020 г. · To evaluate a triple integral in spherical coordinates, use the iterated integral ∫θ=βθ=α∫ρ=g2(θ)ρ=g1(θ)∫u2(r,θ)φ=u1(r,θ)f(ρ,θ,φ)ρ2sinφdφdρdθ.

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 ...

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Опубликовано: 24 нояб. 2012 г.

Converting to spherical coordinates can make triple integrals much easier to work out when the region you are integrating over has some spherical symmetry.