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!