We have started getting volumes and areas using Reiman's sums and then turning them into definite integrals. I get some of this but there is one part when we take the antiderv that is not getting through to me!!!

If we have a hemsishere that has a radius of 7 cm^3 then the volume of a slice would be pi r^2 dh of slice

so our integral would be from 0 to 7 of pi(7^2 -h^2) dh

when this has its antiderv taken the book says it is

pi(7^2h - 1/3h^3 ) from 0 to 7 and then they say this is equal to

2/3 pi7^3

Please tell me how they get this since I thought the h was so small we do not use it and the other term would just equal to pi 7^2 (7)

In other words how do they get the 2/3?????????

THanks for any help you math minded folks can provide!