A 4-sphere (hypersphere) centered at the origin with radius R with coordinates (x, y, z, u) would satisfy the equation x^2 + y^2 + z^2 + u^2 = R^2, where the βtopβ half can be written as u = β(R^2 β x^2 β y^2 β z^2). The volume of this 4-sphere can then be computed as V4(R) = 2β« β« β«Eβ(R^2 β x^2 β y^2 β z^2) dV where E is the projection of the region into R^3, which would be a ball of radius R centered at the origin. This integral can now be evaluated using spherical coordinates. Evaluate this triple integral in spherical coordinates to determine the formula for V4(R). The Ο integral will require the use of trig-substitution and some trig identities.