Let s (z) = A0Z 3+A 1Z 2+A2Z+A3.

Volume v = ∫ (-h/2->; h/2)s(z)dz =∫(-h/2-& gt； h/2)(a0z^3+a 1z^2+a2z+a3)dz

=a 1h^3/ 12+a3h

B 1=s(-h/2)

B2=s(h/2)

M=s(0)

Then b1+B2+4m = s (-h/2)+s (h/2)+4s (0).

=[a0(-h/2)^3+a 1(-h/2)^2+a2(-h/2)+a3]+[a0(h/2)^3+a 1(h/2)^2+a2(h/2)+a3]+4a3

=a 1h^2/2+6a3

(h/6)(b 1+b2+4m)=(h/6)(a 1h^2/2+6a3)=a 1h^3/ 12+a3h

So v = a1h 3/12+a3h = (h/6) (b1+B2+4m).