asteroid = 星芒形

asteroid : x^( 2/3 )+y^( 2/3 ) = a^( 2/3 ) ( a＞0 )

S

= 4∫ y dx ( x = 0〜a )

( x , y )

= ( a( cosθ )^3 , a( sinθ )^3 )

と変換して

S

= 6a^2B( 5/2 , 3/2 )

= 6a^2π/16

= ( 3/8 )πa^2

l

= 4∫ √( ( dx/dθ )^2+( dy/dθ )^2 ) dθ ( θ = 0〜π/2 )

= 6a : πが入らない！