计算(0,π/2)上的积分,然后乘以4即可 S/4 = ∫ y dx = ∫ a(sint)^3 d a(cost)^3 = -3a^2 ∫ sin^4t cos^2t dt = 3a^2 ( x/16 - 1/64 Sin[2 x] - 1/64 Sin[4 x] + 1/192 Sin[6 x] ) =3a^2 * π/32 所以S = 3 πa^2/8
