由对称性,
S＝4∫(0→a)ydx
＝4∫(π/2→0) a(sint)^3 d[a(cost)^3]
＝12a^2×∫(0→π/2) (sint)^4×(cost)^2 dt
＝12a^2×∫(0→π/2) [(sint)^4－(sint)^6] dt
＝12a^2×[3/4×1/2×π/2－5/6×3/4×1/2×π/2]
＝(3πa^2)/8