Question
Write a definite integral in terms of x that represents the volume of a sphere with radius 2.
Answers
Steve
since x^2+y^2+z^2 = 4
using symmetry, we can take 8 times the volume in the first octant. Then v =
8∫[0,2] ∫[0,√(4-x^2)] ∫[0,√(4-x^2-y^2)] dz dy dx
using symmetry, we can take 8 times the volume in the first octant. Then v =
8∫[0,2] ∫[0,√(4-x^2)] ∫[0,√(4-x^2-y^2)] dz dy dx