Write a definite integral in terms of x that represents the volume of a sphere with radius 2.

Answer 1

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