V = 2∫ [x:0,2a]dx ∫ [y:0,√(2ax-xx)]dy √(4ax-yy)
= 2∫ dx ∫ d(y/√(4ax)) 4ax √( 1 - (y/√(4ax))^2 )
= 4a ∫ dx x { asin(s) + s √(1-ss) } (∵ ①②)
= 64 a^3 ∫ [s:0,1/√2]ds (s-2s^3){ asin(s) + s√(1-ss) }
= 32 a^3 ∫ d{ (ss-s^4)(asin(s) + s√(1-ss)) } - ∫ ds 2(ss-s^4)√(1-ss)
= 32 a^3 { (π/16 + 1/8) - (1/8)(π/4 + 1/3) } (∵ ⑤)
= a^3 (π + 8/3)