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Date: 14-2-2021
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Volume integrals
A volume integral takes the form
(1.1)
where V is some volume and dV = dx dy dz is a small volume element. The volume element is sometimes written d3r, or even dτ. As an example of a volume integral, let us evaluate the centre of gravity of a solid hemisphere of radius a. The height of the centre of gravity is given by
(1.2)
The bottom integral is simply the volume of the hemisphere, which is 2πa3/3. The top integral is most easily evaluated in spherical polar coordinates, for which z = r cos θ and dV = r2 sin θ dr dθ dϕ. Thus,
(1.3)
giving
(1.4)
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دراسة: عدم ترتيب الغرفة قد يدل على مشاكل نفسية
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علماء: تغير المناخ تسبب في ارتفاع الحرارة خلال موسم الحج
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ضمن مؤتمر الإمام الباقر (عليه السلام).. أكاديمي يناقش التربية العقدية في سلوك الآل المحمدي
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