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. |
31 авг. 2016 г. · In order to integrate a function f(r,θ,φ) on the unit sphere centred at the origin you have to calculate: ∫1r=0∫πθ=0∫2πφ=0f(r,θ,φ)⋅r2sinθ dφdθdr ... |
6 мар. 2013 г. · I'm going over asks to find the volume of the below solid 1. by using a triple integral with spherical coordinates, and 2. by using a triple integral with ... |
8 июн. 2019 г. · It should be vol(BR)=∫R−R∫√R2−z2−√R2−z2∫√R2−z2−y2−√R2−z2−y2dxdydz. The way to think about this is to successively "fix" each variable as ... |
2 мая 2014 г. · Integrating the surface equation gives you the volume that the surface encloses like when you integrate the function of a graph you obtain the area under the ... |
9 июн. 2021 г. · Since the volume of a cube whose side is 2R is 8R3(=(2R)3) and since the volume of a sphere with radius R is 43πR3, you can just take∫R−R∫R−R∫R− ... |
8 апр. 2019 г. · This is by far easiest in spherical coordinates, as long as you use the correct volume element of drrsinθdrrdϕ=r2sinθdrdθdϕ rather than ... |
11 мая 2022 г. · The volume is give by V=∭EdV. where E is the solid built by above of the cone z=√x2+y2 and inside of the sphere x2+y2+z2=42. |
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