d[a(sint)^3]=3a(sint)^2*costdt,d[a(cost)^3]=-3a(cost)^2sintdt,所以原式=6a^2∫<0,π/2>[(sint)^2(cost)^4+(sint)^4(cost)^2]dt=(3/2)a^2∫<0,π/2>(sin2t)^2dt=(3/4)a^2∫<0,π/2>(1-cos4t）dt=3πa^2/8.
