Integrate = x1 dx2 ^ dx3 + x2 dx3 ^ dx1 + x3 dx1 ^ dx2 over a region of the sphere of radius

Integrate α = x1 dx2 ^ dx3 + x2 dx3 ^ dx1 + x3 dx1 ^ dx2 over a region of the sphere of radius a (from initial φ to final φ, from initial θ to final θ). Note: All the numbers are subscripts and the ^ are wedge products.