联立 y = x^2/2, x^2+y^2=8, 容易求得抛物线和圆交点: A (-2, 2), B (2, 2)
蓝加紫部分,积分求得面积 S1 = ∫(-2 -> 2) (2 - x^2/2) dx
红加紫部分,面积 S2 为圆面积的 1/4, S2 = πR^2/4 = 8π/4 = 2π
紫色部分,面积 S3 为三角形面积 S3 = R^2/2 = 4
所求面积,S = S1 + S2 - S3
S1 = ∫(-2 -> 2) (2 - x^2/2) dx = (2x - x^3/6) | (-2 -> 2) = 16/3
S = 16/3 + 2π - 4 = 4/3 + 2π
至于剩下(抛物线下,圆以内)的面积,就是圆面积 8π - S = 6π - 4/3