The biggest question in spherical coordinates: Why is the differential ρ^2sinθ dρdθdφ?

Описание к видео The biggest question in spherical coordinates: Why is the differential ρ^2sinθ dρdθdφ?

We know the differential volume in the rectangular coordinate system is just dx dy dz but what is it in the spherical coordinate system? Many calculus have learned that dx dy dz = ρ^2sinθ dρ dθ dφ but why do we need the ρ^2sinθ ? This multivariable calculus tutorial provides a geometric approach to understanding the dV in the spherical coordinate system. Make sure you subscribe to ‪@bprpcalculusbasics‬ because we will do the dV by using the Jacobian soon!
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