∫[-√2→√2] √(8-2y²) dy =√2∫[-√2→√2] √(4-y²) dy 令y=2sinu,则√(4-y²)=2cosu,dy=2cosudu,u:-π/4→π/4 =√2∫[-π/4→π/4] 4cos²u du 利用奇偶对称性 =8√2∫[0→π/4] cos²u du =4√2∫[0→π/4] (1+cos2u) du =4√2(u+(1/2)sin2u) |[0→π/4] =4√2(π/4+1/2) =√2π+2√2
∫[-√2→√2] √(8-2y²) dy =√2∫[-√2→√2] √(4-y²) dy 令y=2sinu,则√(4-y²)=2cosu,dy=2cosudu,u:-π/4→π/4 =√2∫[-π/4→π/4] 4cos²u du 利用奇偶对称性 =8√2∫[0→π/4] cos²u du =4√2...