[:) ?] wedge_volume = integral(triangle_area, x=-r_sphere..+r_sphere) triangle_area = 1/2 r_slice^2 dtheta r_slice = sqrt(r_sphere^2 - x^2) wedge_volume = I{-r_sphere..+ triangle_area dx wedge_volume = I{-r_sphere..+ 1/2 r_slice^2 dtheta dx wedge_volume = I{-r_sphere..+ 1/2 sqrt(r_sphere^2 - x^2)^2 dtheta dx wedge_volume = I{-r_sphere..+ 1/2 (r_sphere^2 - x^2) dtheta dx so one integral is represented, but hte other isn't. the dtheta integral is missing. i guess it would make sense to have put it in ....... no wait, we're consider a differential volume, there should be only one integral. we'll integrate dtheta later. given rules of multiplication i think i can factor the dtheta out of the integral? wedge_volume = dtheta/2 I{-r_sphere..+ (r_sphere^2 - x^2) dx i would put next step right here, but it seems other parts put it in separate thing. [maybe in middle is